Exhibit 4.1

FIRST AMENDMENT TO

RIGHTS AGREEMENT

This FIRST AMENDMENT TO RIGHTS AGREEMENT (this “Amendment”) entered into as of November 10, 2015, by and between Theravance Biopharma, Inc., a Cayman Islands exempted company (the “Company”), and Computershare Inc., a Delaware corporation (the “Rights Agent”). All capitalized terms used herein and not otherwise defined shall have the meaning ascribed to them in that certain Rights Agreement dated as of May 9, 2014 (the “Rights Agreement”).

RECITALS

WHEREAS, the Company and the Rights Agent are parties to the Rights Agreement.

WHEREAS, the Company has authorized an amendment of the definition of “Acquiring Person” in the Rights Agreement to increase the beneficial ownership threshold in such definition from 19% to 19.9%.

WHEREAS, pursuant to Section 27 of the Rights Agreement, the Company and the Rights Agent desire to amend the Rights Agreement as set forth in this Amendment.

NOW, THEREFORE, in consideration of the promises and the mutual agreements herein set forth, the parties hereby agree as follows:

1.                                      Amendment of Section 1(a) . The definition of “Acquiring Person” set forth in Section 1(a) of the Rights Agreement is hereby amended and restated to read in its entirety as follows:

“(a)    Acquiring Person” shall mean any Person (as such term is hereinafter defined) who or which, together with all Affiliates and Associates of such Person, shall be the Beneficial Owner (as such term is hereinafter defined) of 19.9% or more of the Ordinary Shares then outstanding, but shall not include an Exempt Person (as such term is hereinafter defined); provided, however, that (i) if the Board of Directors of the Company determines in good faith that a Person who would otherwise be an “Acquiring Person” became the Beneficial Owner of a number of Ordinary Shares such that the Person would otherwise qualify as an “Acquiring Person” inadvertently (including, without limitation, because (A) such Person was unaware that it beneficially owned a percentage of Ordinary Shares that would otherwise cause such Person to be an “Acquiring Person” or (B) such Person was aware of the extent of its Beneficial Ownership of Ordinary Shares but had no actual knowledge of the consequences of such Beneficial Ownership under this Agreement) and without any intention of changing or influencing control of the Company, then such Person shall not be deemed to be or to have become an “Acquiring Person” for any purposes of this Agreement unless and until such Person shall have failed to divest itself, as soon as practicable (as determined, in good faith, by the Board of Directors of the Company), of Beneficial Ownership of a sufficient number of Ordinary Shares so that such Person would no longer otherwise qualify as an “Acquiring Person”; (ii) if, as of the date hereof or prior to the first public

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announcement of the adoption of this Agreement, any Person is or becomes the Beneficial Owner of 19.9% or more of the Ordinary Shares outstanding, such Person shall not be deemed to be or to become an “Acquiring Person” unless and until such time as such Person shall, after the first public announcement of the adoption of this Agreement, become the Beneficial Owner of additional Ordinary Shares (other than pursuant to a dividend or distribution paid or made by the Company on the outstanding Ordinary Shares or pursuant to a split or subdivision of the outstanding Ordinary Shares), unless, upon becoming the Beneficial Owner of such additional Ordinary Shares, such Person is not then the Beneficial Owner of 19.9% or more of the Ordinary Shares then outstanding; (iii) no Person shall become an “Acquiring Person” as the result of an acquisition of Ordinary Shares by the Company which, by reducing the number of shares outstanding, increases the proportionate number of Ordinary Shares beneficially owned by such Person to 19.9% or more of the Ordinary Shares then outstanding, provided, however, that if a Person shall become the Beneficial Owner of 19.9% or more of the Ordinary Shares then outstanding by reason of such share acquisitions by the Company and shall thereafter become the Beneficial Owner of any additional Ordinary Shares (other than pursuant to a dividend or distribution paid or made by the Company on the outstanding Ordinary Shares or pursuant to a split, subdivision or recapitalization of the outstanding Ordinary Shares), then such Person shall be deemed to be an “Acquiring Person” unless upon becoming the Beneficial Owner of such additional Ordinary Shares such Person does not beneficially own 19.9% or more of the Ordinary Shares then outstanding; (iv) no Person shall become an “Acquiring Person” solely as a result of any unilateral grant of any security by the Company or through the exercise of any options, warrants, rights or similar interests (including restricted shares) granted by the Company to its directors, officers and employees; (v) no Person shall become an “Acquiring Person” as the result of the acquisition of Beneficial Ownership of the Ordinary Shares from an individual who, on the later of the date hereof or the first public announcement of this Agreement, is the Beneficial Owner of 19.9% or more of the Ordinary Shares then outstanding if such Ordinary Shares are received by such Person upon such individual’s death pursuant to such individual’s will or pursuant to a charitable trust created by such individual for estate planning purposes and (vi) Glaxo Group Limited (“GGL”) and GlaxoSmithKline plc (together with GGL, “GSK”), together with its Affiliates and Associates, shall not be deemed an “Acquiring Person” for purposes of this Agreement (x) for so long as GGL is in compliance with the terms of that certain Governance Agreement dated March 3, 2014 by and among the Company and GGL (the “Governance Agreement”), and (y) if on the date of termination of the Governance Agreement, GSK, together with its Affiliates and Associates, is the Beneficial Owner of 19.9% or more of the Ordinary Shares outstanding, GSK, together with its Affiliates and Associates, shall not be deemed to be or to become an “Acquiring Person” unless and until such time as GSK or any of its Affiliates or Associates shall, after termination of the Governance Agreement, become the Beneficial Owner of additional Ordinary Shares (other than pursuant to a dividend or distribution paid or made by the Company on the outstanding Ordinary Shares or pursuant to a split or subdivision of the outstanding Ordinary Shares), unless, upon becoming the Beneficial Owner of such additional Ordinary Shares, GSK, together with its Affiliates and Associates, is not then the Beneficial Owner of 19.9% or more of the Ordinary Shares then outstanding.  For all purposes of this Agreement, any

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calculation of the number of Ordinary Shares outstanding at any particular time, including for purposes of determining the particular percentage of such outstanding Ordinary Shares of which any Person is the Beneficial Owner, shall be made in accordance with the last sentence of Rule 13d-3(d)(1)(i) of the General Rules and Regulations under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), as in effect on the date hereof.”

2.                                      Amendment of Exhibit C (Summary of Rights) . Exhibit C to the Rights Agreement is hereby updated with the Summary of Rights attached hereto as Exhibit A.

3.                                      Agreement as Amended . The term “Agreement” as used in the Rights Agreement shall be deemed to refer to the Rights Agreement as amended hereby. Except as set forth herein, the Rights Agreement shall remain in full force and effect and otherwise shall be unaffected hereby, and each of the Company and the Rights Agent shall continue to be subject to its terms and conditions.

4.                                      Severability . If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated; provided, that if any such excluded terms, provisions, covenants or restrictions shall affect the rights, immunities, liabilities, duties, responsibilities or obligations of the Rights Agent, the Rights Agent shall be entitled to resign immediately.

5.                                      Governing Law . This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts to be made and performed entirely within such State; provided , however , that all provisions regarding the Rights Agent’s rights, immunities, liabilities, duties, responsibilities or obligations hereunder shall be governed by and construed in accordance with the laws of the State of New York applicable to contracts made and to be performed entirely within such state.

6.                                      Counterparts . This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument. A signature to this Amendment executed and/or transmitted electronically shall have the same authority, effect, and enforceability as an original signature.

7.                                      Descriptive Headings . Descriptive headings of the several Sections of this Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

[Signatures begin on following page]

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

EXHIBIT A

UNDER CERTAIN CIRCUMSTANCES, AS SET FORTH IN THE RIGHTS AGREEMENT, RIGHTS OWNED BY OR TRANSFERRED TO ANY PERSON WHO IS OR BECOMES AN ACQUIRING PERSON OR AN AFFILIATE OR ASSOCIATE THEREOF (AS THOSE TERMS ARE DEFINED IN THE RIGHTS AGREEMENT) AND CERTAIN TRANSFEREES THEREOF WILL BECOME NULL AND VOID AND WILL NO LONGER BE TRANSFERABLE.

SUMMARY OF RIGHTS TO PURCHASE

PREFERRED SHARES OF

THERAVANCE BIOPHARMA, INC.

On May 4, 2014 the Board of Directors of Theravance Biopharma, Inc. (the “Company”) authorized and granted to the sole shareholder of the Company one preferred share purchase right (a “Right”) for each outstanding Ordinary Share, par value $0.00001 per share, of the Company (the “Ordinary Shares”).  The grant was effected on May 9, 2014 (the “Record Date”) to the shareholders of record on that date.  Each Right entitles the registered holder to purchase from the Company one one-thousandth of a share of Series A Junior Participating Preferred Share, par value $0.00001 per share, of the Company (the “Preferred Share”) at a price of $225.00 per one one-thousandth of a Preferred Share (the “Purchase Price”), subject to adjustment.  The description and terms of the Rights are set forth in a Rights Agreement dated as of May 9, 2014, as the same may be amended from time to time (the “Rights Agreement”), between the Company and Computershare Inc., as Rights Agent (the “Rights Agent”).

Until the earlier to occur of (i) 10 days following a public announcement that a person or group of affiliated or associated persons (with certain exceptions, an “Acquiring Person”) has acquired beneficial ownership of 19.9% or more of the outstanding Ordinary Shares or (ii) 10 business days (or such later date as may be determined by action of the Board of Directors prior to such time as any person or group of affiliated persons becomes an Acquiring Person) following the commencement of, or announcement of an intention to make, a tender offer or exchange offer the consummation of which would result in the beneficial ownership by a person or group of 19.9% or more of the outstanding Ordinary Shares (the earlier of such dates being called the “Distribution Date”), the Rights will be evidenced, with respect to any of the Ordinary Shares certificates outstanding as of the Record Date, by such Ordinary Shares certificate together with this Summary of Rights.

The Rights Agreement provides that, until the Distribution Date (or earlier expiration of the Rights), the Rights will be transferred with and only with the Ordinary Shares.  Until the Distribution Date (or earlier expiration of the Rights), new Ordinary Shares certificates issued after the Record Date upon transfer or new issuances of Ordinary Shares will contain a notation incorporating the Rights Agreement by reference.  Until the Distribution Date (or earlier expiration of the Rights), the surrender for transfer of any certificates for Ordinary Shares outstanding as of the Record Date, even without such notation or a copy of this Summary of Rights, will also constitute the transfer of the Rights associated with the Ordinary Shares represented by such certificate.  As soon as practicable following the Distribution Date, separate

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certificates evidencing the Rights (“Right Certificates”) will be mailed to holders of record of the Ordinary Shares as of the close of business on the Distribution Date and such separate Right Certificates alone will evidence the Rights.

The Rights are not exercisable until the Distribution Date.  The Rights will expire on May 9, 2024 (the “Final Expiration Date”), unless the Final Expiration Date is advanced or extended or unless the Rights are earlier redeemed or exchanged by the Company, in each case as described below.

The Purchase Price payable, and the number of Preferred Shares or other securities or property issuable, upon exercise of the Rights is subject to adjustment from time to time to prevent dilution (i) in the event of a share dividend on, or a subdivision, combination or reclassification of, the Preferred Share, (ii) upon the grant to holders of the Preferred Shares of certain rights or warrants to subscribe for or purchase Preferred Shares at a price, or securities convertible into Preferred Shares with a conversion price, less than the then-current market price of the Preferred Shares or (iii) upon the distribution to holders of the Preferred Shares of evidences of indebtedness or assets (excluding regular periodic cash dividends or dividends payable in Preferred Shares) or of subscription rights or warrants (other than those referred to above).

The number of outstanding Rights is subject to adjustment in the event of a share dividend on the Ordinary Shares payable in Ordinary Shares or subdivisions, consolidations or combinations of the Ordinary Shares occurring, in any such case, prior to the Distribution Date.

Preferred Shares purchasable upon exercise of the Rights will not be redeemable.  Each Preferred Share will be entitled, when, as and if declared, to a minimum preferential quarterly dividend payment of the greater of (a) $1.00 per share, and (b) an amount equal to 1,000 times the dividend declared per Ordinary Share.  In the event of liquidation, dissolution or winding up of the Company, the holders of the Preferred Shares will be entitled to a minimum preferential payment of the greater of (a) $10.00 per share (plus any accrued but unpaid dividends), and (b) an amount equal to 1,000 times the payment made per Ordinary Share.  Each Preferred Share will have 1,000 votes, voting together with the Ordinary Shares.  Finally, in the event of any merger, consolidation or other transaction in which outstanding Ordinary Shares are converted or exchanged, each Preferred Share will be entitled to receive 1,000 times the amount received per Ordinary Share.  These rights are protected by customary anti-dilution provisions.

Because of the nature of the Preferred Share’s dividend, liquidation and voting rights, the value of the one one-thousandth interest in a Preferred Share purchasable upon exercise of each Right should approximate the value of one Ordinary Share.

In the event that any person or group of affiliated or associated persons becomes an Acquiring Person, each holder of a Right, other than Rights beneficially owned by the Acquiring Person (which will thereupon become void), will thereafter have the right to receive upon exercise of a Right that number of Ordinary Shares having a market value of two times the exercise price of the Right.

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In the event that, after a person or group has become an Acquiring Person, the Company is acquired in a merger or other business combination transaction or 50% or more of its consolidated assets or earning power are sold, proper provisions will be made so that each holder of a Right (other than Rights beneficially owned by an Acquiring Person which will have become void) will thereafter have the right to receive upon the exercise of a Right that number of Ordinary Shares of the person with whom the Company has engaged in the foregoing transaction (or its parent) that at the time of such transaction have a market value of two times the exercise price of the Right.

At any time after any person or group becomes an Acquiring Person and prior to the earlier of one of the events described in the previous paragraph or the acquisition by such Acquiring Person of 50% or more of the outstanding Ordinary Shares, the Board of Directors of the Company may exchange the Rights (other than Rights owned by such Acquiring Person which will have become void), in whole or in part, for Ordinary Shares or Preferred Shares (or a series of the Company’s preferred shares having equivalent rights, preferences and privileges), at an exchange ratio of one Ordinary Share, or a fractional Preferred Share (or other preferred shares) equivalent in value thereto, per Right.

With certain exceptions, no adjustment in the Purchase Price will be required until cumulative adjustments require an adjustment of at least 1% in such Purchase Price.  No fractional Preferred Shares or Ordinary Shares will be issued (other than fractions of Preferred Shares which are integral multiples of one one-thousandth of a Preferred Share, which may, at the election of the Company, be evidenced by depositary receipts), and in lieu thereof an adjustment in cash will be made based on the current market price of the Preferred Shares or the Ordinary Shares.

At any time prior to the time an Acquiring Person becomes such, the Board of Directors of the Company may redeem the Rights in whole, but not in part, at a price of $.01 per Right (the “Redemption Price”) payable, at the option of the Company, in cash, Ordinary Shares or such other form of consideration as the Board of Directors of the Company shall determine.  The redemption of the Rights may be made effective at such time, on such basis and with such conditions as the Board of Directors in its sole discretion may establish.  Immediately upon any redemption of the Rights, the right to exercise the Rights will terminate and the only right of the holders of Rights will be to receive the Redemption Price.

For so long as the Rights are then redeemable, the Company may, except with respect to the Redemption Price, amend the Rights Agreement in any manner.  After the Rights are no longer redeemable, the Company may, except with respect to the Redemption Price, amend the Rights Agreement in any manner that does not adversely affect the interests of holders of the Rights.

Until a Right is exercised or exchanged, the holder thereof, as such, will have no rights as a shareholder of the Company, including, without limitation, the right to vote or to receive dividends.

A copy of the form of Rights Agreement has been filed with the Securities and Exchange Commission as an Exhibit to the Company’s Registration Statement on Form 10 dated April 30,

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2014.  A copy of the Rights Agreement is available free of charge from the Company.  This summary description of the Rights does not purport to be complete and is qualified in its entirety by reference to the Rights Agreement, as the same may be amended from time to time, which is hereby incorporated herein by reference.

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