Strategic Rights Letter Agreement, by and between the Company and Astellas, dated August 4, 2023

Exhibit 10.3

EXECUTION VERSION

CERTAIN INFORMATION CONTAINED IN THIS EXHIBIT, MARKED BY [***], HAS BEEN EXCLUDED FROM THIS EXHIBIT BECAUSE THE REGISTRANT HAS DETERMINED THAT IT IS BOTH NOT MATERIAL AND IS THE TYPE THAT THE REGISTRANT TREATS AS PRIVATE OR CONFIDENTIAL.

August 4, 2023

Astellas US LLC

2375 Waterview Drive

Northbrook Illinois, 60062

Attention: President

Re:    Strategic Rights

Ladies and Gentlemen:

This strategic rights letter agreement (this “Letter Agreement”) will confirm our agreement that as partial inducement for Astellas US LLC (“Astellas”) to enter into that certain Securities Purchase Agreement, dated as of the date hereof, by and between Poseida Therapeutics, Inc., a Delaware corporation (the “Company”), and Astellas (the “Purchase Agreement”), the Company shall grant Astellas certain rights pursuant to the terms and conditions set forth in this Letter Agreement. Each of Astellas and the Company are also referred to herein individually as a “Party” and together as the “Parties.”

1.        Consideration. As partial consideration for the rights granted to Astellas hereunder, Astellas shall pay the Company a one-time payment in the amount of Twenty-five Million Dollars ($25,000,000) on the Closing Date (as defined in the Purchase Agreement) (the “Upfront Payment”).

2.            Board Observer Rights.

2.1.    Following the Closing Date, Astellas shall have the right, but not the obligation, to designate a representative reasonably acceptable to the Company to attend all meetings of (i) the Company’s Board of Directors (the “Board of Directors”), (ii) any committees of the Board of Directors, and (iii) the Company’s Scientific Advisory Board, in each case, in a non-voting observer capacity (the “Board Observer”) and, in this respect, the Board Observer shall be entitled to receive copies of all notices, minutes, consents, and other materials that the Company provides to its directors in connection with such meetings at the same time and in the same manner such notices, minutes, consents and other materials are provided to the Board of Directors; provided that the Board Observer shall agree to hold in confidence and not use all information so provided pursuant to the terms of a customary confidentiality agreement in a form reasonably acceptable to the Company executed by such Board Observer, and provided further that the Company reserves the right to withhold any information and to exclude such representative from any meeting or portion thereof if […***…]. Astellas acknowledges and agrees that all minutes and Board materials relating to any Change in Control transaction relating to Astellas or other potential Change in Control transaction of the Company may be withheld from such Board Observer. Astellas may remove or replace the Board Observer at any time upon advance written notice to the Company; provided, that such Board Observer is reasonably acceptable to

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the Company and such replacement Board Observer agrees to hold in confidence and not use all information so provided pursuant to the terms of a confidentiality agreement in the same form or substantially similar form entered into by the prior Board Observer to be executed by such replacement Board Observer.

3.        Change in Control Notice.

3.1.    During the period beginning on the Closing Date and ending on the 18-month anniversary of the Closing Date (or, if there is no corresponding date in such calendar month, then the last day of such calendar month) (the “CIC Notification Period”), the Company grants Astellas a right of notification with respect to a Change in Control, as set forth in Section 3.2 and subject to the terms and conditions set forth in this Letter Agreement. For purposes of this Letter Agreement, the term “Change in Control” means (i) a consolidation, merger or similar transaction of the Company with or into any other corporation or other entity or Person (as defined in the Purchase Agreement), except for any such consolidation, merger or similar transaction involving the Company in which the shares of capital stock of the Company outstanding immediately prior to such consolidation, merger or similar transaction continue to represent, or are converted into or exchanged for shares of capital stock that represent, immediately following such consolidation, merger or similar transaction, a majority, by voting power, of the capital stock of (a) the surviving or resulting corporation, or (b) if the surviving or resulting corporation is a wholly owned subsidiary of another corporation immediately following such consolidation, merger or similar transaction, the parent corporation of such surviving or resulting corporation; (ii) any transaction or series of related transactions in which fifty percent (50%) or more of the Company’s voting power is transferred or becomes beneficially owned by any Person or group; or (iii) the sale or transfer of all or substantially all of the Company’s assets or the exclusive, worldwide license of all or substantially all of the Company intellectual property related to the Company’s cell therapy programs that is material to the Company and its subsidiaries, taken as a whole.

3.2.    Subject to Section 7, during the CIC Notification Period, the Company agrees to promptly provide written notice (a “Potential CIC Notice”) to Astellas (i) each time the Company receives a bona fide written offer for a Change in Control from any third party (a “Third Party”), unless such bona fide written offer is rejected by the Board of Directors; or (ii) of the commencement of a sales process for a Change in Control approved by the Board of Directors. If the Company gives to Astellas a Potential CIC Notice of the commencement of a sales process for a Change in Control, […***…]. Each Potential CIC Notice shall also indicate whether the Company intends to enter into discussions with such Third Party to consummate a Change in Control. To the extent the Company provides access to a virtual data room or otherwise provides the Company’s confidential information to a Third Party in connection with Change in Control, the Company shall provide prompt written notice to Astellas that it intends to provide such information, and thereafter, shall provide virtual data room access to Astellas to the same confidential information provided to such Third Party (subject to any limitations for competitively sensitive information in order to comply with antitrust laws) concurrently when such access is being provided to the Third Party. The Company will not be obligated to disclose the terms of any bona fide offer received from a Third Party or the identity of the Third Party, if any, in any Potential CIC Notice.

4.        Program Notice; Exclusivity.

4.1.    During the period beginning on the Closing Date and ending on the earlier of (i) a Change in Control and (ii) the twelve (12) month anniversary of the Closing Date (or, if there is no corresponding date in such calendar month, then the last day of such calendar month) (the “Exclusivity Period”), the Company hereby agrees that it shall not (a) solicit, knowingly encourage, negotiate or otherwise enter into bona fide discussions about a Program Transaction with any Third Party, (b) provide access to any Company confidential information relating to the Program for purposes of knowingly facilitating a Program Transaction, or (c) enter into any letter of intent, contract

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or other commitment for a Program Transaction. For purposes of this Letter Agreement, the term “Program Transaction” means (i) the Company granting to a Third Party an exclusive or co-exclusive license or the entry of a co-promotion or co-marketing arrangement or otherwise granting commercial rights to a Third Party to sell, promote or market one or more products of the Company’s P-MUC1C-ALLO1 development program (the “Program”) for any indication anywhere in the world; (ii) the Company’s sale, assignment or transfer (or grant of an option exercisable by a Third Party to acquire any material portion of the assets of the Program) to a Third Party; or (iii) the Company entering into any exclusive master distribution agreement or other similar exclusive commercial partnership for the Program for any indication anywhere in the world.

4.2.    During the period beginning on the Closing Date and ending on the earlier of (i) a Change in Control and (ii) the eighteen (18) month anniversary of the Closing Date (or, if there is no corresponding date in such calendar month, then the last day of such calendar month) (the “Program Notification Period”), the Company agrees to promptly provide written notice to Astellas of (i) any bona fide proposal for a Program Transaction received from a Third Party unless such proposal is rejected by the Board of Directors (the “Program Transaction Proposal”); or (ii) following the Exclusivity Period, the commencement of substantive discussions for a Program Transaction with a Third Party by members of the Company’s executive management team in connection with the commencement of a process to pursue a Program Transaction approved by the Board of Directors (the “Program Process”). […***…].

5.        Program Right of First Offer.

5.1.    During the Program Notification Period and following receipt pursuant to Section 4.2 of written notice from the Company of the Program Process (the “ROFO Notice”), the Company shall provide Astellas a right of first offer to negotiate a Program Transaction before the Company engages with any Third Party in meaningful substantive discussions (including potential economics) regarding a potential Program Transaction. From receipt of the ROFO Notice to […***…] thereafter (the “ROFO Interest Exercise Period”), Astellas shall have the option to notify the Company in writing of its interest in negotiating a Program Transaction (the “ROFO Interest Notice”).

5.2.    If Astellas provides a ROFO Interest Notice within the ROFO Interest Exercise Period, the Company shall within […***…] thereafter provide Astellas with access to a virtual data room for the Program containing due diligence information typically provided for transactions of such nature, subject to implementing processes (such as execution by Astellas of a standard non-disclosure and non-use agreement, the use of a clean team, aggregating information and redactions), and make relevant personnel of the Company reasonably available to Astellas or its representatives to answer Astellas’ questions relating to the contents of the virtual data room and the Program. From initial receipt of access to the virtual data room to […***…] thereafter (the “ROFO Election Exercise Period”), Astellas shall have the option to notify the Company of its election to proceed with the negotiation of a Program Transaction (the “ROFO Election Notice”).

5.3.    If Astellas provides a ROFO Election Notice within the ROFO Election Exercise Period, the Company shall grant Astellas exclusive negotiation rights and negotiate exclusively with Astellas in good faith concerning the terms of such Program Transaction for a period of […***…] (the “ROFO Negotiation Period”). During the ROFO Negotiation Period, the Company shall continue to make available to Astellas or its representatives relevant personnel of the Company during reasonable times and with reasonable advance notice, to answer Astellas’ questions relating to the contents of the virtual data room and the Program.

5.4.    If Astellas (i) at any point during the process outlined in this Section 5, notifies the Company that it does not desire to negotiate a Program Transaction, (ii) fails to timely deliver the ROFO Interest

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Notice to the Company during the ROFO Interest Exercise Period, (iii) fails to timely deliver the ROFO Election Notice to the Company during the ROFO Election Exercise Period, or (iv) timely delivers a ROFO Interest Notice and a ROFO Election Notice to the Company, but the Parties are unable to reach agreement on the terms of such Program Transaction prior to the expiration of the ROFO Negotiation Period, then the Company shall be free to enter into a Program Transaction with another Third Party; provided that if the discussions terminate pursuant to (iv) only, the terms of such Program Transaction with such Third Party entered into within […***…] after such termination shall contain terms and conditions (including financial) that are, in the aggregate, more favorable to the Company than those last offered by Astellas during the ROFO Negotiation Period.

6.        Program Right of First Refusal.

6.1.    During the Program Notification Period and following receipt pursuant to Section 4.2 of a written notice from the Company of a Program Transaction Proposal (the “ROFR Notice”), the Company shall provide Astellas a right of first refusal (the “Right of First Refusal”) to negotiate a Program Transaction before the Company, following the end of the Exclusivity Period, enters into a term sheet, letter of intent or similar written arrangement with the Third Party that submitted the Program Transaction Proposal that was the subject of the ROFR Notice. For Clarity, nothing contained in this paragraph shall limit or modify the restrictions of the Company during the Exclusivity Period contained in Section 4.1. From initial receipt of the ROFR Notice to […***…] thereafter (the “ROFR Interest Exercise Period”), Astellas shall have the option to notify the Company in writing of its interest in negotiating a Program Transaction (the “ROFR Interest Notice”).

6.2.    If Astellas provides a ROFR Interest Notice within the ROFR Interest Exercise Period, the Company shall within […***…] thereafter provide Astellas with access to a virtual data room for the Program containing due diligence information typically provided for transactions of such nature, subject to implementing processes (such as execution by Astellas of a standard non-disclosure and non-use agreement, the use of a clean team, aggregating information and redactions), and make relevant personnel of the Company reasonably available to Astellas or its representatives to answer Astellas’ questions relating to the contents of the virtual data room and the Program. From receipt of access to the virtual data room to […***…] thereafter (the “ROFR Election Exercise Period”), Astellas shall have the option to notify the Company of its desire to exercise its Right of First Refusal (the “ROFR Election Notice”).

6.3.    Following delivery of the ROFR Election Notice within the ROFR Election Exercise Period, Astellas may, in its sole discretion but not later than the […***…] following delivery of the ROFR Election Notice, deliver to the Company an offer in writing (the “Astellas Offer”) for a competing Program Transaction. If the Astellas Offer contains terms and conditions (including financial) that are, in the aggregate, more favorable to the Company than the Program Transaction Proposal, then the Company shall grant Astellas exclusive negotiation rights for […***…] (the “ROFR Negotiation Period”). During the ROFR Negotiation Period, the Company shall negotiate exclusively and in good faith with Astellas with respect to entering into a mutually acceptable definitive, written agreement with respect to a Program Transaction, and the Company shall not (i) solicit, knowingly encourage, negotiate or enter into bona fide discussions about a Program Transaction with any Third Party, (ii) enter into any letter of intent, contract or other commitment for a Program Transaction with any Third Party or grant any rights of exclusive dealing to any Third Party regarding the Program Transaction Proposal, or (ii) take any action that would reasonably be anticipated to frustrate or materially impede Astellas’ exercise of its Right of First Refusal until after expiration of the ROFR Interest Exercise Period or, in the event Astellas timely provides the ROFR Interest Notice, the ROFR Election Exercise Period, or in the event Astellas timely provides its ROFR Election Notice, expiration of the ROFR Negotiation Period (provided that entering into a definitive agreement for a Change in Control shall not be deemed to frustrate or materially impede Astellas’ exercise of its Right of First Refusal).

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6.4.    If at any point during the process outlined in this Section 6, Astellas (i) notifies the Company that it does not wish to negotiate a Program Transaction, (ii) fails to timely deliver the ROFR Interest Notice to the Company during the ROFR Interest Exercise Period, (iii) fails to timely deliver a ROFR Election Notice to the Company during the ROFR Election Exercise Period, or (iv) timely delivers a ROFR Interest Notice and a ROFR Election Notice to the Company, but the Parties are unable to reach agreement on the terms of such Program Transaction prior to the expiration of the ROFR Negotiation Period, then the Right of First Refusal shall automatically terminate and the Company shall be free to enter into a Program Transaction with another Third Party; provided that if the Right of First Refusal terminates in accordance with (iv) the terms of such Program Transaction with such Third Party entered into with […***…] after such termination shall contain terms and conditions (including financial) that are, in the aggregate, more favorable to the Company than those last offered by Astellas during the ROFR Negotiation Period.

7.      Conduct of Phase 1 Clinical Trial and Access to Data. The Company hereby covenants and agrees to use commercially reasonable efforts to conduct its ongoing P-MUCIC-ALLO1 Phase 1 dose escalating study (the “Program Trial”) in accordance with the study protocol as it may be modified from time to time and the summary development plan attached as Exhibit B, and in accordance with the timelines set forth therein. The Company shall provide written copies to Astellas of any proposed changes to the study protocol prior to submission to any regulatory authority, and a reasonable opportunity for Astellas to discuss with the Company the proposed changes and the rationale for the proposed changes prior to submission to any relevant regulatory authority. The Company shall make available Kristin Yarema, President of Cell Therapy, or another knowledgeable executive to provide monthly updates to Astellas on the conduct of the Program Trial and the data generated in connection therewith. At the request of Astellas, the Company shall provide to Astellas true, correct and complete copies of the patient data generated by the Company as such data becomes available to the Company; […***…].

8.        Off-Set. Astellas or any of its Affiliates (as defined in the Purchase Agreement) shall have the right, in its or their discretion and upon written notice to the Company, to offset the Payment Amount (in whole or in part, until the full amount of the Payment Amount has been offset) against (a) any payment(s) owed by Astellas to the Company or any of its controlled affiliates under or in connection with any Program Transaction, including, any upfront payment, milestone payment or royalties owed to the Company or any of its controlled affiliates or (b) any amount owed by Astellas to the Company or any of its controlled affiliates in connection with a Change in Control transaction with Astellas or any of its Affiliates. For purposes of this Section 8, the Payment Amount equals […***…].

9.      Termination. This Letter Agreement shall be effective as of the date hereof and shall continue in effect until and shall terminate upon the earliest to occur of (i) the 18-month anniversary of the Closing Date (or, if there is no corresponding date in such calendar month, then the last day of such calendar month), (ii) such time that Astellas and its Affiliates own fewer than 8,000,000 shares of the Company’s common stock (subject to adjustment for any stock splits, stock dividends or recapitalizations) and (iii) the consummation of a Change in Control. Termination of this Letter Agreement for any reason shall be without prejudice to any rights that shall have accrued to the benefit of a Party prior to such termination. Without limiting the foregoing, Sections 5.4, 6.4 (in each case, in accordance with the time periods set forth therein) and 8 shall survive the termination of this Letter Agreement.

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10.        Research Collaboration. […***…].

11.        Miscellaneous.

11.1.    Assignment. This Letter Agreement may not be assigned in whole or in part by either Party without the prior written consent of the other Party; provided, that Astellas may assign this Letter Agreement in whole or in part to any of its Affiliates without the prior consent of the Company; thereafter it shall be binding upon the Parties, and the successors and assigns of both Parties.

11.2.    Governing Law; Jurisdiction. This Letter Agreement shall be governed by, and construed in accordance with, the internal laws of the State of Delaware without regard to the choice of law principles thereof. Each of the Parties hereto irrevocably submits to the exclusive jurisdiction of the Delaware Chancery Court (or, if the Delaware Chancery Court shall be unavailable, then any federal court of the United States of America sitting in the State of Delaware) for the purpose of any suit, action, proceeding or judgment relating to or arising out of this Letter Agreement and the transactions contemplated hereby. Service of process in connection with any such suit, action or proceeding may be served on each Party hereto anywhere in the world by the same methods as are specified for the giving of notices under this Letter Agreement. Each of the Parties hereto irrevocably consents to the jurisdiction of any such court in any such suit, action or proceeding and to the laying of venue in such court. Each Party hereto irrevocably waives any objection to the laying of venue of any such suit, action or proceeding brought in such courts and irrevocably waives any claim that any such suit, action or proceeding brought in any such court has been brought in an inconvenient forum.

11.3.    Notices. Any and all notices or other communications or deliveries required or permitted to be provided hereunder shall be in writing and shall be deemed given and effective on the earliest of (i) the date of transmission, if such notice or communication is delivered via email at the email address specified in this Section prior to 4:00 p.m. (California time) on a Business Day (as defined in the Purchase Agreement), (ii) the next Business Day after the date of transmission, if such notice or communication is delivered via email at the email address specified in this Section on a day that is not a Business Day or later than 4:00 p.m. (California time) on any Business Day, (iii) the Business Day following the date of deposit with a nationally recognized overnight courier service, or (iv) upon actual receipt by the Party to whom such notice is required to be given. The addresses and email addresses for such notices and communications are those set forth below, or such other address or email address as may be designated in writing hereafter, in the same manner, by any such Person:

If to the Company:

Poseida Therapeutics, Inc.

9390 Towne Centre Drive, Suite 200

San Diego, California 92121

Attention: Chief Executive Officer

Email:

with a copy to (which copy shall not constitute notice):

Cooley LLP

10265 Science Center Drive

San Diego, California 92121

Attention: Thomas A. Coll

Email: ***@***

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If to Astellas:

Astellas US LLC

2375 Waterview Drive

Northbrook, IL 60062

Attention: President

Email:

with a copy to (which copy shall not constitute notice):

Astellas US LLC

2375 Waterview Drive

Northbrook, IL 60062

Attention: General Counsel

Email:

11.4.     Amendments; Waivers. This Letter Agreement and any term hereof may be amended, terminated, or waived only with the written consent of the Company and Astellas. No waiver of any default with respect to any provision, condition or requirement of this Letter Agreement shall be deemed to be a continuing waiver in the future or a waiver of any subsequent default or a waiver of any other provision, condition or requirement hereof, nor shall any delay or omission of either Party to exercise any right hereunder in any manner impair the exercise of any such right.

11.5. Counterparts; Execution. This Letter Agreement may be executed in two (2) or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument. Counterparts may be delivered via electronic mail (including pdf or any electronic signature complying with the U.S. federal ESIGN Act of 2000, e.g., www.docusign.com) or other transmission method and any counterpart so delivered shall be deemed to have been duly and validly delivered and be valid and effective for all purposes.

11.6. Severability. If any provision hereof should be held invalid, illegal or unenforceable in any respect, then, to the fullest extent permitted by law, (a) all other provisions hereof shall remain in full force and effect and shall be liberally construed in order to carry out the intentions of the Parties as nearly as may be possible and (b) the Parties shall use their best efforts to replace the invalid, illegal or unenforceable provision(s) with valid, legal and enforceable provision(s) which, insofar as practical, implement the purposes of such provision(s) in this Letter Agreement.

[SIGNATURE PAGE TO FOLLOW]

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Exhibit A

Development Plan

[…***…]