Exhibit 4.1

Execution

ISSUING AND PAYING

AGENCY AGREEMENT

between

TEXAS CAPITAL BANK, N.A.

as Issuer,

and

U.S. BANK NATIONAL ASSOCIATION

as Issuing and Paying Agent and Note Registrar

THIS ISSUING AND PAYING AGENCY AGREEMENT, made and dated as of January 31, 2014, between, Texas Capital Bank, N.A., a national banking association, as Issuer (the “Issuer”), and U.S. Bank National Association, as the Issuing and Paying Agent and Note Registrar (hereinafter sometimes called, in each such capacity, the “Agent”).

WHEREAS, the Issuer intends to issue and sell its 5.25% Subordinated Notes due 2026 (the “Bank Notes”), pursuant to the offering circular, dated January 28, 2014 (the “Offering Circular”);

NOW, THEREFORE, in consideration of the covenants and agreements made herein, the parties hereto agree as follows:

Section 1.  Definitions . The words and terms used herein unless otherwise defined herein shall have the respective meanings assigned to such terms in the Bank Notes.

Section 2.  Appointment and Acceptance . The Issuer hereby appoints U.S. Bank National Association as Issuing and Paying Agent and Note Registrar with respect to the Bank Notes, upon the terms and conditions set forth herein, and U.S. Bank National Association hereby accepts such appointment and agrees to perform all of the duties of Issuing and Paying Agent and Note Registrar in accordance with the terms of the Bank Notes and this Agreement.

Section 3.  Form of Note Certificates . The Issuer shall deliver to the Agent completed Bank Notes executed by manual or facsimile signature of an officer of the Issuer duly authorized to execute the Bank Notes together with an order requesting the Agent to authenticate such Bank Notes (an “Authentication Order”). Such Bank Notes will be in such form as the Issuer shall deliver to the Agent.

Any Bank Note bearing the manual or facsimile signature of a person who is duly authorized to execute such Bank Note on the date such signature is affixed shall bind the Issuer after the completion thereof by the Agent notwithstanding that such person shall have ceased to hold his or her office on the date such Bank Note is countersigned and delivered by the Agent.

Unless the Issuer notifies the Agent to the contrary, all Bank Notes will be represented by one note certificate, hereinafter called the “Global Note.” The Global Note shall be registered in the name of a nominee of The Depository Trust Company (“DTC”), as Depositary. Beneficial interests in the Global Note will be shown on, and transfers thereof will be effected only through, records maintained by DTC and its participants.

Section 4.  Certificate of Authorized Representatives of the Issuer . The Issuer shall from time to time furnish the Agent with a certificate of the Issuer certifying the incumbency and specimen signatures of representatives of the Issuer authorized to instruct the Agent regarding the completion and delivery of the Bank Notes (each, an “Authorized Representative”). The Agent shall have no responsibility to the Issuer to determine whether a signature of an Authorized Representative is genuine if such signature resembles the specimen signature of such Authorized Representative on such certificate.

Section 5.  Duties of Issuing Agent: Completion, Authentication and Delivery .

(a) The Global Note shall be issued and delivered in accordance with the Blanket Letter of Representations from the Issuer to DTC dated as of January 30, 2014. All instructions regarding the completion and delivery of the Global Note shall be given by an Authorized Representative by facsimile or other means acceptable to the Agent. All Authentication Orders with respect to the completed Global Note delivered for authentication to the Agent shall be in writing and shall be executed by an Authorized Representative. Upon receipt of instructions as described above, the Agent shall:

(1) manually countersign the Global Note by any one of the officers or employees of the Agent duly authorized and designated by it for such purpose; and

(2) deliver the Global Note to DTC or hold on behalf of DTC pursuant to DTC’s instructions.

(b) The Agent shall incur no liability to the Issuer in acting hereunder upon any instructions or Authentication Order contemplated hereby which the Agent believed in good faith to have been given by an Authorized Representative.

(c) Each instruction or Authentication Order given to the Agent in accordance with this Section 5 shall constitute a representation and warranty to the Agent by the Issuer that the issuance and delivery of the Bank Note or Notes to which the instruction or Authentication Order relates have been duly and validly authorized by the Issuer, that such Bank Note or Notes when completed, countersigned and delivered pursuant hereto, will constitute the legal, valid and binding obligations of the Issuer, and that the Agent’s appointment to act for the Issuer hereunder has been duly authorized by all necessary corporate action of the Issuer.

Section 6.  Duties of Note Registrar: Registration, Registration of Transfer and Exchange . The Agent, in its capacity as Note Registrar, shall, so long as any of the Bank Notes remain outstanding, subject without limitation to Section 3 above, maintain all records as may be customary or provided to it, including all forms of transfer, probates, letters of administration and powers of attorney, and shall:

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(a) Keep at its Paying Agent Office in Dallas, Texas (the “Paying Agent Office”), a register (the “Note Register”) in such form as the Agent may determine, in which, subject to reasonable regulations as it may prescribe, it shall provide for the registration of Bank Notes and of transfers of Bank Notes;

(b) Maintain records showing for each outstanding Bank Note the principal amount and other terms thereof; all subsequent transfers and changes of ownership thereof; and the name, address and tax identification number of the registered holder of such Bank Note (each, a “Holder”);

(c) Record any transfer of Bank Notes which it believes in good faith to have been duly authorized; provided that, the Agent may refuse to record any transfer of the Bank Notes if in good faith the Agent deems such refusal necessary in order to avoid any liability either to the Issuer or to itself;

(d) Prepare all such lists of Holders as may be required by the Issuer or any person needing such information and so authorized in writing by the Issuer; and

(e) During regular office hours and upon reasonable prior written notice, make the Note Register available to the Issuer or any person needing such information and so authorized in writing by the Issuer for inspection and for the taking of copies thereof; provided that the Agent shall have no responsibility or liability for any aspect of the records relating to or payments made on account of beneficial ownership interests in the Global Note or for maintaining, supervising or reviewing any records relating to such beneficial ownership interests, and it shall be fully protected in acting or refraining from acting on any such information provided by DTC.

Upon surrender for registration of transfer of any Bank Note at the Paying Agent Office, the Issuer shall execute, and the Agent shall authenticate and deliver, in the name of the designated transferee or transferees, one or more new Bank Notes of authorized denominations (which in no case may be less than $250,000 and integral multiples of $1,000 in excess thereof) and of a like tenor and aggregate principal amount; provided that, unless and until it is exchanged in whole or in part for individual Bank Notes represented thereby, the Global Note may not be transferred except as a whole by DTC to a nominee of DTC, or by a nominee of DTC to DTC or another nominee of DTC, or by DTC or any such nominee to a successor depositary or a nominee of such successor depositary.

If (i) DTC notifies the Issuer in writing that it is unwilling or unable to act as Depositary or DTC ceases to be a clearing agency registered under the Securities Exchange Act of 1934, as amended, and a successor depositary is not appointed by the Issuer within 90 days, (ii) the Issuer, at its option, notifies the Agent in writing that it elects to cause the issuance of Bank Notes in definitive form or (iii) any event shall have happened and be continuing that, after notice or lapse of time or both, would constitute an Event of Default with respect to the Bank Notes, then, upon surrender by DTC or a successor depositary of the Global Notes, the Agent

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shall authenticate and deliver Bank Notes, upon receipt of instructions from the Issuer, of like tenor and terms in definitive form in an aggregate principal amount equal to the principal amount of the Global Note outstanding in exchange for such Global Note, to each person that DTC or a successor depositary identifies as the beneficial owner of the related Bank Notes.

Upon the exchange of the Global Note for Bank Notes in definitive form upon the occurrence of any of the events described above, the Global Note shall be cancelled by the Agent. Bank Notes issued in exchange for the Global Note shall be registered in such names and in such authorized denominations, and delivered to such addresses, as DTC, pursuant to instructions from its direct or indirect participants or otherwise, shall instruct the Agent in writing. The Agent shall deliver such Bank Notes to the persons in whose names such Bank Notes are registered or to DTC, in fully registered form without coupons in denominations of $250,000 or any amount in excess thereof that is an integral multiple of $1,000. Such Bank Notes may not subsequently be exchanged by a Holder for Bank Notes in denominations of less than $250,000.

In case any Bank Note shall at any time become mutilated, destroyed, lost or stolen and such Bank Note or evidence satisfactory to the Issuer of the loss, theft or destruction thereof (together with indemnity satisfactory to the Agent and the Issuer and such other documents or proof as may be required by the Agent and the Issuer) shall be delivered to the Agent and the Issuer, the Agent shall authenticate and deliver, upon receipt of instructions from the Issuer, a new Bank Note of like tenor in exchange for the Bank Note so mutilated, or in lieu of the Bank Note so destroyed or lost or stolen.

Section 7.  Duties of Paying Agent: Payment of Bank Notes . Payment of principal (and premium, if any) and interest on the Bank Notes shall be made by the Agent in the manner and on the dates specified in the Bank Notes from funds deposited by the Issuer with the Agent for such payments as provided in Section 8. The Agent shall have no obligation to use its own funds for any such payment of principal, premium or interest on the Bank Notes. Payments due at the maturity or redemption of a Bank Note shall be made only upon presentation and surrender of such Bank Note. Any money that the Issuer pays to the Agent for the purpose of making payments on the Bank Notes and that remains unclaimed two years after the payments were due will, at the Issuer’s request, be returned to it. After that time any Holders of such Bank Notes can only look to the Issuer for payment on such Bank Notes.

Section 8.  Deposit of Funds . The Issuer shall deposit with the Agent by 9:30 a.m., New York time (i) on each Interest Payment Date (as such term is defined in such Bank Note) of a Bank Note an amount in immediately available funds sufficient to pay the interest due on such date and (ii) on the Maturity Date (as such term is defined in such Bank Note) or earlier redemption date an amount in immediately available funds sufficient to pay the principal of such Bank Note, the premium due thereon, if any, and the interest accrued thereon to such Maturity Date or redemption date, as the case may be. The Agent shall clearly identify in its books and records funds relating to the Bank Notes. At the Issuer’s request, any money that the Issuer pays to the Agent for the purpose of making payments on Bank Notes and that remains unclaimed two years after the payments were due shall be returned to the Issuer (after which time a Holder may only look to the Issuer for payment on Bank Notes).

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Section 9.  Fees and Expenses of the Agent . The Issuer shall pay such fees and expenses of the Agent for the performance of its duties as Issuing and Paying Agent and Note Registrar hereunder as may be mutually agreed upon from time to time in writing.

Section 10.  Conditions . The Agent accepts its obligations herein set forth upon the terms and conditions hereof, including the following, to all of which the Issuer agrees:

Section 11.  Indemnification . Notwithstanding any satisfaction or discharge of any Bank Notes, the Issuer shall indemnify the Agent and its directors, officers, agents and employees against any and all loss, liability, costs, damages, claims, actions, expenses or demands which it may incur or sustain or which may be made against it in connection with its appointment or the exercise of its powers and duties hereunder as well as the reasonable costs, including the expenses and fees of counsel in defending any claim, action or demand, except such as may result from the willful misconduct, gross negligence, bad faith or reckless disregard by the Agent or any of its officers, employees or agents of any of the Agent’s duties, responsibilities or obligations under this Agreement. The Agent shall incur no liability and shall be indemnified and held harmless by the Issuer for, or in respect of, any actions taken or suffered to be taken in good faith by the Agent in accordance herewith and in reliance upon the written opinion or advice of counsel or (ii) written instructions that, after reasonable investigation, are believed to be duly authorized by the Issuer.

Section 12.  Resignation or Removal of the Agent .

(a) Except as provided below, the Agent may at any time resign as Note Registrar, as Issuing Agent or as Paying Agent by giving written notice to the Issuer of its intention to resign from any or all such offices, specifying the date on which its desired resignation shall become effective; provided that such notice shall be given not less than 45 days prior to the said effective date unless the Issuer otherwise agrees in writing. Except as provided below, the Agent may be removed from any or all of the offices to which it is hereby appointed by the Issuer delivering to the Agent an instrument in writing signed by the Issuer specifying such removal and the date when it shall become effective (such effective date being at least 20 days after said filing).

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(b) If at any time the Agent shall resign or be removed from any or all of the offices to which it is hereby appointed, then a successor Note Registrar, Issuing Agent or Paying Agent, as the case may be, shall be appointed by the Issuer by an instrument in writing delivered to the successor Note Registrar, Issuing Agent or Paying Agent, as the case may be. Upon the appointment as aforesaid of a successor Note Registrar, Issuing Agent or Paying Agent, as the case may be, and acceptance by the latter of such appointment, the former Note Registrar, Issuing Agent or Paying Agent, as the case may be, shall cease to hold such office.

(c) Any successor Note Registrar, Issuing Agent or Paying Agent appointed hereunder shall execute and deliver to its predecessor and the Issuer an instrument accepting such appointment hereunder, and thereupon such successor Note Registrar, Issuing Agent or Paying Agent, without any further act, deed or conveyance, shall become vested with all the authority, rights, powers, immunities, duties and obligations of such predecessor with like effect as if originally named as the Note Registrar, Issuing Agent or Paying Agent hereunder, and such predecessor shall thereupon become obligated to transfer and deliver, and such successor shall be entitled to receive, copies of any relevant records maintained by such predecessor Note Registrar, Issuing Agent or Paying Agent.

(d) Any corporation into which the Agent may be merged or converted or any corporation with which the Agent may be consolidated or any corporation resulting from any merger, conversion or consolidation to which the Agent shall be a party shall, to the extent permitted by applicable law, be the successor Note Registrar, Issuing Agent or Paying Agent under this Agreement without the execution or filing of any paper or any further act on the part of any of the parties hereto. Notice of any such merger, conversion or consolidation shall forthwith be given to the Issuer.

(e) The provisions of Section 11 hereof shall survive any resignation or removal hereunder and the termination of this Agreement with respect to matters occurring prior to any such resignation or removal and the termination of this Agreement.

Section 13.  Event of Default Notification . The Issuer will promptly notify the Agent upon the occurrence of an Event of Default or of the curing of an Event of Default, and the Issuer will provide copies of any such notice of the occurrence of an Event of Default or the curing of an Event of Default to the Agent, whereupon the Agent will promptly mail by first-class mail, postage prepaid, copies of such notice to the Holders of the Bank Notes in the Note Register at their respective addresses appearing in the Agent’s records.

Section 14.  Notices . All notices, instructions and communications between the parties hereto in connection with this Agreement shall be delivered in person, sent by letter, facsimile or communicated by telephone (subject, in the case of communication by telephone, to written confirmation dispatched within two Business Days by letter or facsimile), in the case of the Issuer, to it at 2000 McKinney Avenue, Suite 700, Dallas, Texas 75201, Attention: Peter B. Bartholow, with a copy to Bracewell & Giuliani LLP, 1445 Ross Avenue, Suite 3800, Dallas, Texas 75202-2711, Attention: Michael W. Tankersley, and in the case of the Agent, to it at 13737 Noel Road, Suite 800, Dallas, Texas 75240, Attention: Global Corporate Trust Services.

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Section 15.  Successors and Assigns . The rights, duties and obligations of the Issuer and the Agent hereunder shall inure, without further act, to their respective successors and assigns.

Section 16.  Amendments . This Agreement may be amended only by an instrument in writing signed by the Issuer and the Agent.

Section 17.  Counterparts . This Agreement may be executed in one or more counterparts and, if executed in one or more counterparts, the executed counterparts shall each be deemed to be an original but all such counterparts shall together constitute one and the same instrument.

Section 18.  GOVERNING LAW . THIS AGREEMENT SHALL BE GOVERNED BY, AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

[signature page follows]

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be executed as of the day and year first above written.

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Exhibit 4.2

TEXAS CAPITAL BANK, N.A.

5.25% SUBORDINATED BANK NOTE DUE 2026

CUSIP No. 88224P JS9

ISIN No. US88224PJS92

THIS SECURITY IS A GLOBAL SECURITY AND IS REGISTERED IN THE NAME OF A DEPOSITARY OR A NOMINEE OF A DEPOSITARY. UNLESS AND UNTIL IT IS EXCHANGED IN WHOLE OR IN PART FOR SECURITIES IN CERTIFICATED FORM, THIS SECURITY MAY NOT BE TRANSFERRED EXCEPT AS A WHOLE BY THE DEPOSITARY TO A NOMINEE OF THE DEPOSITARY OR BY A NOMINEE OF THE DEPOSITARY TO THE DEPOSITARY OR ANOTHER NOMINEE OF THE DEPOSITARY OR BY THE DEPOSITARY OR ANY SUCH NOMINEE TO A SUCCESSOR DEPOSITARY OR A NOMINEE OF SUCH SUCCESSOR DEPOSITARY.

UNLESS THIS SECURITY IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY TO TEXAS CAPITAL BANK, N.A., OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY SECURITY ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR SUCH OTHER NAME AS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY (AND ANY PAYMENT IS MADE TO CEDE & CO. OR SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY) ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR TO ANY PERSON IS WRONGFUL SINCE THE REGISTERED OWNER HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

THE OBLIGATION EVIDENCED BY THIS SECURITY IS NOT A DEPOSIT OR A SAVINGS ACCOUNT AND IS NOT INSURED OR GUARANTEED BY THE FEDERAL DEPOSIT INSURANCE CORPORATION OR ANY OTHER GOVERNMENT AGENCY.

THE OBLIGATION EVIDENCED BY THIS SECURITY IS SUBORDINATED TO THE CLAIMS OF DEPOSITORS AND GENERAL CREDITORS OF TEXAS CAPITAL BANK, N.A., EXCEPT LIABILITIES WHICH BY THEIR TERMS RANK EQUALLY WITH OR ARE SUBORDINATE TO THE NOTES, AND IS INELIGIBLE AS COLLATERAL TO SECURE A LOAN BY TEXAS CAPITAL BANK, N.A.

TEXAS CAPITAL BANK, N.A., a national banking association (herein called the “Bank”), for value received, hereby promises to pay or deliver, as the case may be, to CEDE & CO., or registered assigns, the principal sum of One Hundred Seventy-Five Million ($175,000,000) United States dollars on the maturity date shown above (the “Maturity Date”) and to pay interest thereon from and including the Issue Date specified above (the “Issue Date”) or from and including the most recent Interest Payment Date to which interest on this Security or any predecessor Security has been paid or duly provided for, but excluding, the succeeding Interest Payment Date, on the Interest Payment Dates specified above in each year (each, an “Interest Payment Date”) and at the Stated Maturity, at the rate per annum equal to 5.25%, until the principal hereof is paid or duly made available for payment. The interest so payable, and punctually paid or duly provided for, on any Interest Payment Date will be paid to the person in whose name this Security (or any predecessor Security) is registered (the “Holder”) at the close of business on the fifteenth calendar day next preceding such Interest Payment Date (the “Regular Record Date”); provided, however, that interest payable at the Maturity Date of this Security will be payable to the person to whom principal shall be payable. Any such interest not so punctually paid or duly provided for shall forthwith cease to be payable to the Holder on such Regular Record Date and may either be paid to the person in whose name this Security (or any predecessor Security) is registered at the close of business on a special record date for the payment of such defaulted interest (the “Special Record Date”) to be fixed by the Bank, notice of which shall be given to the Holder not less than 10 calendar days prior to such Special Record Date, or be paid at any time in any other lawful manner.

Interest shall accrue from and including January 31, 2014 or from and including the most recent Interest Payment Date to which interest has been paid or duly provided for, and shall be paid semi-annually in arrears on each January 31 and July 31, commencing July 31, 2014. Interest will be computed on the basis of a 360-day year consisting of twelve 30-day months.

If an Interest Payment Date is not a Business Day (as defined below), the Bank will pay interest on the next day that is a Business Day, with the same force and effect as if made on the Interest Payment Date, and without any interest or other payment with respect to the delay. If the Maturity Date falls on a day that is not a Business Day, the payment of principal and interest, if any, will be made on the next succeeding Business Day, and no interest shall accrue and be payable for the period from and after such Maturity Date.

“Business Day” means, any day that is not a Saturday or Sunday and that is not a day on which banking institutions in the City of New York, New York generally are authorized or obligated by law or executive order to close.

TO THE EXTENT THEN REQUIRED UNDER OR PURSUANT TO APPLICABLE CAPITAL REGULATIONS, THIS SECURITY MAY NOT BE REPAID PRIOR TO MATURITY, EITHER PURSUANT TO ACCELERATION IN AN EVENT OF DEFAULT OR OTHERWISE, WITHOUT THE PRIOR WRITTEN APPROVAL OF THE OFFICE OF THE COMPTROLLER OF THE CURRENCY (THE “OCC”).

Payment of principal of and premium, if any, and interest on, this Security will be made in such coin or currency of the United States of America as at the time of payment is legal tender for payment of public and private debts. The Bank will at all times appoint and maintain an issuing and paying agent (the “Issuing and Paying Agent”) authorized by the Bank to pay the principal of, and interest on, this Security on behalf of the Bank and having an office or agency (the “Issuing and Paying Agent Office”) in the United States of America (the “Place of Payment”), where this Security may be presented or surrendered for payment and where notices, designations or requests in respect of payments with respect to this Security may be served. The Bank has initially appointed U.S. Bank National Association, as such Issuing and Paying Agent pursuant to the Issuing and Paying Agency Agreement, dated as of January 31, 2014 (the “Issuing and Paying Agency Agreement”), between the Bank and the Issuing and Paying Agent, with the Issuing and Paying Agent Office currently located at 13737 Noel Road, Suite 800, Dallas, TX 75240.

Payment of the principal of, and premium, if any, and interest on, this Security due at maturity will be made in immediately available funds upon presentation and surrender of this Security to the Issuing and Paying Agent at the Issuing and Paying Agent Office in the Place of Payment; provided that this Security is presented to the Issuing and Paying Agent in time for the Issuing and Paying Agent to make such payment in accordance with its normal procedures. Payments of interest on this Security (other than at maturity) will be made by wire transfer to such account as has been appropriately designated to the Issuing and Paying Agent by the person entitled to such payments.

Subject to required approvals, the Bank may, without the consent of the Holder of this Security, create and issue additional notes ranking equally with this Security and otherwise similar in all respects (except for the issue date and issue price), provided that any such additional notes are fungible with the Notes for U.S. Federal income tax purposes. Such further notes shall be consolidated and form a single series with this Security,

Reference is hereby made to the further provisions of this Security set forth on the reverse hereof, which further provisions shall for all purposes have the same effect as if set forth at this place.

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Unless the certificate of authentication hereon has been executed by the Issuing and Paying Agent by the manual signature of an authorized signatory, this Security shall not be valid or obligatory for any purpose.

IN WITNESS WHEREOF, the Bank has caused this instrument to be duly executed by manual or facsimile signature.

Dated: January 31, 2014

ISSUING AND PAYING AGENT’S CERTIFICATE OF AUTHENTICATION

This is one of the Securities referred to in the within-mentioned Issuing and Paying Agency Agreement.

U.S. BANK NATIONAL ASSOCIATION, as Issuing and Paying Agent

REVERSE OF SECURITY

This Security is one of a duly authorized issue of 5.25% Subordinated Bank Notes Due 2026 of the Bank (the “Securities”) issued under the Issuing and Paying Agency Agreement.

Subordination

The indebtedness of the Bank evidenced by this Security, including principal, premium, if any, and interest, is unsecured and subordinate and junior in right of payment to the Bank’s obligations to its depositors, its obligations under banker’s acceptances, letters of credit, including its obligations to any Federal Reserve Bank, to the FDIC and any rights acquired by the FDIC as a result of loans made or other assistance provided by the FDIC to the Bank or the purchase or guarantee of any of its assets by the FDIC pursuant to the provisions of 12 U.S.C. Section 1823(c), (d) or (e), and its obligations to its other creditors, whether now outstanding or hereafter incurred (except any obligations which expressly rank on a parity with or junior to this Security, including the Capital Notes (as defined below). In the event of any insolvency proceedings, receivership, conservatorship, reorganization, readjustment of debt, marshalling of assets and liabilities or similar proceedings or any liquidation, dissolution or winding up of or relating to the Bank, whether voluntary or involuntary, all such obligations (except obligations which expressly rank on a parity with or junior to the Securities, including the Capital Notes) shall be entitled to be paid in full before any payment shall be made on account of the principal of, or premium, if any, or interest on this Security. Such prior obligations include all borrowed money, similar obligations arising from off-balance sheet guarantees and direct-credit substitutes, and obligations associated with derivative products such as interest rate and foreign-exchange contracts, commodity contracts and similar arrangements. In the event of any such proceeding, after payment in full of all sums owing with respect to such prior obligations, the Holder of this Security, together with holders of any obligations of the Bank ranking on a parity with this Security, including the Capital Notes, shall be entitled to be paid from the remaining assets of the Bank the unpaid principal of, and the unpaid premium, if any, and interest on, this Security or such other obligations, before any payment or other distribution, whether in cash, property, or otherwise, shall be made on account of any capital stock or any obligations of the Bank ranking junior to this Security.

“Capital Notes” means the unsecured Capital-Qualified Subordinated Notes issued by the Bank to Texas Capital Bancshares, Inc. (“TCBI”) from time to time, evidencing certain of TCBI’s capital investments in the Bank. At December 31, 2013, $260.0 million in Capital Notes were outstanding. The Capital Notes are subordinated to the claims of the Bank’s depositors and other creditors substantially to the same extent as the Securities and rank pari passu with the Securities. The Bank may from time to time issue additional Capital Notes to TCBI that would rank pari passu with the Securities, or could borrow from TCBI pursuant to instruments that would be senior in right of payment to the Securities.

Nothing herein shall impair the obligation of the Bank, which is absolute and unconditional, to pay the principal of and any premium and interest on this Security in accordance with its terms.

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Notwithstanding any other provisions of this Security, it is expressly understood and agreed that the OCC or any receiver or conservator of the Bank appointed by the OCC shall have the right in the performance of its legal duties, and as a part of any transaction or plan of reorganization or liquidation designed to protect or further the continued existence of the Bank or the rights of any parties or agencies with an interest in, or claim against, the Bank or its assets, to transfer or direct the transfer of the obligations represented by this Security to any national banking association, state bank or bank holding company selected by the OCC or any such receiver or conservator which shall expressly assume the obligation of the due and punctual payment of the unpaid principal, premium, if any, and interest on this Security and the due and punctual performance of all covenants and conditions herein; and the completion of such transfer and assumption shall serve to supersede and void any default, acceleration or subordination which may have occurred, or which may occur due or related to such transaction, plan, transfer or assumption, pursuant to the provisions of this Security, and shall serve to return the Holder hereof to the same position, other than for substitution of the obligor, it would have occupied had no default, acceleration or subordination occurred; except that any interest and principal (and premium, if any) previously due, other than by reason of acceleration, and not paid shall, in the absence of a contrary agreement by the Holder of this Security, be deemed to be immediately due and payable as of the date of such transfer and assumption, together with the interest from its original due date at the rate provided for herein.

Any depository institution, as that term is defined in Section 3(c)(1) of the Federal Deposit Insurance Act, which holds a Security (or beneficial interest therein) shall be deemed to have agreed by acquiring such Security (or beneficial interest) that any rights of such institution to offset all or any portion of the indebtedness represented by such Security (or interest) against any indebtedness or other obligations of such institution to the Bank are waived by such institution.

Event of Default; Waiver

An “Event of Default” with respect to this Security shall occur only if the Bank consents to, or a court or other governmental agency enters a decree or order for, the appointment of a receiver, liquidator, trustee, or other similar official in any receivership, liquidation, insolvency or similar proceeding with respect to the Bank or all or substantially all of its property, and, in the case of an order or decree, such order or decree shall have remained in force for a period of 60 days. The Bank will promptly notify, and provide copies of such notice to, the Issuing and Paying Agent, upon the occurrence of any Event of Default. The Issuing and Paying Agent will promptly mail copies of such notice to the Holders of the Securities.

If an Event of Default shall occur and be continuing, the Holder of this Security may declare the principal of this Security, together with any unpaid accrued interest thereon, to be immediately due and payable by written notice to the Bank. Upon such declaration and notice such principal amount and accrued interest shall become immediately due and payable; provided, however, that, to the extent then required under or pursuant to applicable capital regulations, this Security may not be repaid prior to maturity without the prior written approval of the OCC. The Bank will apply to the OCC for prior written approval of repayment promptly after receiving notice of acceleration.

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Any Event of Default with respect to this Security may be waived by the Holder hereof.

The Bank waives demand, presentment for prepayment, notice of nonpayment, notice of protest and all other notices to the extent it may lawfully do so.

Redemption

The Securities shall not be redeemable at the option of the Bank prior to their stated maturity except that the Bank may redeem the Securities in whole, but not in part, at the Bank’s option prior to the Maturity Date at a redemption price equal to 100% of the principal amount of the Securities together with accrued but unpaid interest to, but excluding, the date fixed for redemption within 90 days of the occurrence of a “regulatory event.” A “regulatory event” means the Bank’s good faith determination that, as a result of (i) any change in or amendment to the laws (or any regulations promulgated under those laws) of the United States or any political subdivision thereof that is enacted or becomes effective after the issuance of Securities (ii) any proposed change in those laws or regulations that is announced after the initial issuance of the Securities; or (iii) any official administrative decision or judicial decision or administrative action or other official pronouncement interpreting or applying those laws or regulations that is announced after the issuance of the Securities, there is more than an insubstantial risk that the Bank will not be entitled to treat the full principal amount of the Securities as “Tier 2 capital” (or its equivalent) of the Bank for purposes of the capital adequacy regulations of the OCC, as then in effect and applicable to the Bank (or, as and if applicable, the capital adequacy regulations of any successor federal banking agency having jurisdiction over the Bank, as then in effect and applicable), for as long as the Securities are outstanding.

The Holder of the Security will receive notice of any redemption by first class mail at least 30 days and not more than 60 days before the date fixed for redemption. On and after the redemption date, interest will cease to accrue on the Notes or any portion of the Notes called for redemption unless the Bank defaults in the payment of the redemption price and accrued interest.

Miscellaneous

This Security is not redeemable or subject to repayment at the option of the Holder, in whole or in part, prior to maturity, and is not subject to any sinking fund.

Beneficial interests represented by this Security are exchangeable for definitive Securities in registered form, of like tenor and of an equal aggregate principal amount, only if (x) the Depository Trust Company, as depositary (the “Depositary”), notifies the Bank in writing that it is unwilling or unable to act as a depositary or the Depositary ceases to be a clearing agency registered under the Securities Exchange Act of 1934, as amended, and a successor depositary is not appointed by the Bank within 90 days, (y) the Bank, at its option, notifies the Issuing and Paying Agent in writing that it elects to cause the issuance of Securities in definitive form or (z) any event shall have occurred and be continuing that, after notice or lapse of time or both, would constitute an Event of Default with respect to the Securities. In such circumstances, upon surrender by the Depositary or a successor depositary of the Global Securities, Securities in definitive form will be issued to each person that the Depositary or a successor depositary

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identifies as the beneficial owner of the related Securities. Any Security representing such beneficial interests that is exchangeable pursuant to this paragraph shall be exchangeable in whole for definitive Securities in registered form, of like tenor and of an equal aggregate principal amount, in minimum denominations of $250,000 and integral multiples of $1,000 in excess thereof. Such definitive Securities shall be registered in the name or names of such person or persons as the Depositary shall instruct the Security Registrar (as defined below).

In case any Security shall at any time become mutilated, destroyed, lost or stolen and such Security or evidence satisfactory to the Bank of the loss, theft or destruction thereof (together with indemnity satisfactory to the Issuing and Paying Agent and the Bank and such other documents or proof as may be required by the Issuing and Paying Agent and the Bank) shall be delivered to the Issuing and Paying Agent and the Bank, a new Security of like tenor will be issued by the Bank in exchange for the Security so mutilated, or in lieu of the Security so destroyed or lost or stolen. All expenses and reasonable charges associated with procuring the indemnity referred to above and with the preparation, authentication and delivery of a new Security shall be borne by the Holder of the Security so mutilated, destroyed, lost or stolen. If any Security which has matured or is about to mature shall become mutilated, destroyed, lost or stolen, the Bank may, instead of issuing a substitute Security, pay or authorize the payment of the same (without surrender thereof except in the case of a mutilated Security) upon compliance by the Holder thereof with the provisions of this paragraph.

The Bank shall cause to be kept at the office of the Security Registrar designated below a register (the register maintained in such office or any other office or agency of the Bank in the Place of Payment herein referred to as the “Security Register”) in such form as the Security Registrar may determine, in which, subject to reasonable regulations as it may prescribe, the Security Registrar shall provide for the registration of the Securities and of transfers of the Securities. The Bank has initially appointed the Issuing and Paying Agent “Security Registrar,” pursuant to the Issuing and Paying Agency Agreement, for the purposes of registering the Securities and transfers of the Securities as herein provided.

The transfer of this Security is registrable in the Security Register, upon surrender of this Security for registration of transfer at the office or agency of the Bank in the Place of Payment, duly endorsed by, or accompanied by a written instrument of transfer in form satisfactory to the Bank and the Issuing and Paying Agent duly executed by, the Holder hereof or his attorney duly authorized in writing, and thereupon one or more new Securities of like tenor, of authorized denominations and for the same aggregate principal amount, will be issued to the designated transferee or transferees.

No service charge shall be made for any such registration of transfer or exchange, but the Bank may require payment of a sum sufficient to cover any tax or other governmental charge payable in connection therewith.

Prior to due presentment of this Security for registration of transfer, the Bank, the Issuing and Paying Agent and any agent of the Bank or the Issuing and Paying Agent may treat the person in whose name this Security is registered as the owner hereof for all purposes, whether or not this Security is overdue, and neither the Bank, the Issuing and Paying Agent nor any such agent shall be affected by notice to the contrary.

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No recourse shall be had for the payment of principal or interest on this Security, for any claim based hereon, or otherwise in respect hereof, against any shareholder, employee, agent, officer or director, as such, past, present or future, of the Bank or any successor corporation.

No provision of this Security shall alter or impair the obligation of the Bank, which is absolute and unconditional, to pay the principal of and interest on this Security at the times, place and rate, and in the coin or currency, herein prescribed.

Any money that the Bank pays to the Issuing and Paying Agent for the purpose of making payments on this Security and that remains unclaimed two years after the payments were due will, at the Bank’s request, be returned to it. After that time the Holder can only look to the Bank for payment on this Security.

All notices under this Security shall be in writing and in the case of the Bank, addressed to 2000 McKinney Ave, Suite 700, Dallas, TX 75201 (Attention: Treasurer), or, in the case of the Issuing and Paying Agent at 13737 Noel Road, Suite 800, Dallas, TX 75240 (Attention: Global Corporate Trust Services) or to such other address of the Issuing and Paying Agent as the Issuing and Paying Agent may notify the holders of the Securities. All notices to the Holder of this Security will be given by first-class mail to the address of the Holder as it appears in the Security Register.

This Security shall be governed by and construed in accordance with the laws of the State of New York and, where applicable, the laws of the United States.

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