Amendment No. 1, dated as of October 9, 2024, to Rights Agreement, dated as of October 10, 2023, by and between Tempest Therapeutics, Inc. and Computershare Trust Company, N.A., as rights agent

Exhibit 4.1

AMENDMENT NO. 1 TO RIGHTS AGREEMENT

This AMENDMENT NO. 1 TO RIGHTS AGREEMENT, dated as of October 9, 2024 (this “Amendment”), is made and entered into by and between Tempest Therapeutics, Inc., a Delaware corporation (the “Company”), and Computershare Trust Company, N.A., a federally chartered trust company, as Rights Agent (the “Rights Agent”). Except as otherwise provided herein, capitalized terms used but not otherwise defined in this Amendment shall have the meanings ascribed to such terms in the Agreement (as defined below).

RECITALS

WHEREAS, the Company and the Rights Agent previously entered into that certain Rights Agreement, dated as of October 10, 2023 (as amended or otherwise modified prior to the date hereof, the “Agreement”);

WHEREAS, the Board of Directors of the Company has determined it to be desirable to amend the Agreement on the terms set forth in this Amendment, including in order to extend the Final Expiration Date of the Agreement;

WHEREAS, pursuant to Section 27 of the Agreement, prior to such time as any Person becomes an Acquiring Person, the Company and the Rights Agent may, if the Board of Directors of the Company so directs, from time to time supplement or amend any provision of the Agreement as the Company may deem necessary or desirable without the approval of any holder of the Company or any other Person other than the Rights Agent;

WHEREAS, as of the date hereof, no Person has become an Acquiring Person under the Agreement; and

WHEREAS, pursuant to the terms of the Agreement and in accordance with Section 27 thereof, the Board of Directors of the Company has directed that the Agreement be amended as set forth in this Amendment, and by its execution and delivery hereof, the Company directs the Rights Agent to execute this Amendment.

NOW, THEREFORE, in consideration of the foregoing and the mutual agreements set forth in the Agreement and this Amendment, the parties hereto, intending to be legally bound, hereby agree as follows:

1. Amendments to the Agreement. The Agreement is hereby amended as follows:

“(w) “Final Expiration Date” shall mean immediately following the Company’s 2025 Annual Meeting of Stockholders, or, if Stockholder Approval is obtained, October 10, 2026.”

2. Officer’s Certificate. By executing this Amendment below, the undersigned duly appointed officer of the Company (i) certifies (in her capacity as an officer of the Company and not in her personal capacity) that (A) this Amendment complies with the applicable terms and conditions of the Agreement, including Section 27 of the Agreement, (B) the Rights remain redeemable at the date of this Amendment, and (C) this Amendment does not adversely affect the rights, duties, obligations or immunities of the Rights Agent under the Agreement, and (ii) directs the Rights Agent to execute this Amendment.

3. Interpretation. From and after the execution and delivery of this Amendment, the term “Agreement” as used in the Agreement shall be deemed to refer to the Agreement as amended hereby.

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, then the remainder of the terms, provisions, covenants and restrictions of this Amendment, and of the Agreement, shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

5. Waiver of Notice. The Rights Agent and the Company hereby waive any notice requirement under the Agreement pertaining to the matters covered by this Amendment.

6. Governing Law. Section 32 of the Agreement shall apply mutatis mutandis to this Amendment.

7. Binding Effect. This Amendment shall be binding upon and inure to the benefit of each party hereto, and its respective successors and assigns.

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

9. 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.

10. Effectiveness. This Amendment shall be deemed effective as of the date first written above. Except as expressly set forth herein, all other terms and conditions of the Agreement are unchanged and shall remain in full force and effect in accordance with their terms.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment No. 1 to Rights Agreement to be duly executed as of the day and year first above written.