Offer Letter, by and between the Registrant and Matthew Spear, dated June 13, 2016

Exhibit 10.7

POSEIDA THERAPEUTICS, INC.

June 13, 2016

Matthew Spear, M.D.

4 Top of State Lane

Wilmington, DE 19807

Re:    Employment Terms

Dear Matthew:

On behalf of Poseida Therapeutics, Inc. (the “Company”), I am pleased to offer you employment under the terms set forth in this offer letter agreement (the “Agreement”). These employment terms will be effective as of your start date, which is anticipated to be June 27, 2016.

1.    Employment Position; Duties. You will be employed as the Company’s Chief Medical Officer (“CMO”). In this position, you will report directly to the Company’s President and Chief Operating Officer (the “COO”) and you will have those duties and responsibilities as customary for this position and as may be directed by the Company or the COO. Your work duties will include work for, or on behalf of, affiliates of the Company, such as its parent, subsidiaries and other group affiliates (together, the “Affiliates”). You will work from the Company’s offices in San Diego, California beginning no later than August 1, 2016. During your employment, you will devote your full-time best efforts to the business of the Company.

2.    Base Salary; Employee Benefits; and Business Expenses.

(a)    Base Salary. Your initial base salary will be paid at the annual rate of $370,000.00, less standard payroll deductions and tax withholdings. Your base salary will be paid on the Company’s normal payroll schedule. As an exempt salaried employee, you will be required to work the Company’s normal business hours, and such additional time as appropriate for your work assignments and position. You will not be eligible for extra payment under the overtime laws.

(b)    Employee Benefits. As a regular full-time employee, you will be eligible to participate in the Company’s standard employee benefits (pursuant to the terms and conditions of the benefit plans and applicable policies), as they may be terminated or changed from time to time within the Company’s discretion.

(c)    Business Expenses. Your legitimate and documented business expenses will be reimbursed by the Company as provided under its business expense reimbursement policies. You will be reimbursed for documented moving expenses to San Diego up to a maximum amount of $20,000. Any such reimbursement is subject to your completion of your relocation by March 31, 2017 and submission of documentation sufficient to substantiate any such expenses and compliance with the Company’s expense reimbursement policies and procedures. In the event that your employment with the Company is terminated by the Company for cause or you voluntarily resign, in any event within twenty four months after the date that you relocate, you shall no longer be eligible for any such reimbursements and you shall repay to the Company any relocation expenses previously reimbursed by the Company.

3.    Incentive Compensation. In addition to base salary, you will be eligible to earn discretionary incentive compensation at an annual target amount of up to thirty percent (30%) of your base salary, based on achievement of individual and corporate performance targets, metrics and/or management-by-objectives (“MBO”) to be determined and approved by the Company’s Board of Directors (the “Board”) or the Compensation Committee thereof. Annual incentive compensation is paid on an annual basis, after the close of the fiscal year and after determination by the Board (or the Compensation Committee thereof) of (i) the level of achievement of the applicable individual and corporate performance targets, metrics and/or MBOs, and (ii) the amount of the annual incentive compensation earned by you (if any). No annual incentive compensation is guaranteed and, in addition to the other conditions for earning such compensation, you must remain an employee in good standing of the Company (or one of its Affiliates) on the scheduled annual incentive compensation payment date in order to be eligible for any annual incentive compensation. This annual incentive compensation program will be the only incentive compensation, commissions, or other bonus program that will apply to you.

4.    Equity Award. Subject to approval by the Board, you will be granted an option to purchase 180,000 shares of the Company’s common stock pursuant and subject to the Company’s 2015 Equity Incentive Plan (the “Plan”) and the Company’s standard form of stock option agreement (the “Option”). The Option shall be an incentive stock option to the extent permissible under Section 422 of the Internal Revenue Code of 1986, as amended (the “Code”) and will have an exercise price per share equal to the fair market value of one share of the Company’s common stock as of the date of grant.

5.    Compliance With Proprietary Information Agreement and Company Policies. As a condition of employment, you shall sign and comply with the Employee Proprietary Information and Inventions Agreement (the “Proprietary Information Agreement”) which is attached as Exhibit A. In addition, you are expected to follow the policies and procedures of the Company and its Affiliates, as modified from time to time within the Company’s or Affiliates’ discretion.

6.    Protection of Third Party Information and Outside Activities.

(a)    Third Party Information. In your work for the Company and its Affiliates, you will be expected not to make any unauthorized use or disclosure of any confidential information or materials, including trade secrets, of any former employer or other third party; and not to violate any lawful agreement that you may have with any third party. By signing this Agreement, you represent that you are able to perform your job duties within these guidelines, and you are not in unauthorized possession or control of any confidential documents, information, or other property of any former employer or third party. In addition, you represent that you have disclosed to the Company in writing any agreement you may have with any third party (e.g., a former employer) which may limit your ability to perform your duties to the Company or its Affiliates or which could present a conflict of interest with the Company or its Affiliates, including but not limited to disclosure (and a copy) of any contractual restrictions on solicitations or competitive activities.

(b)    Outside Activities. Throughout your employment with the Company, you may engage in civic and not-for-profit activities so long as such activities do not interfere with the performance of your duties hereunder or present a conflict of interest with the Company or its Affiliates. Subject to the restrictions set forth herein, and only with prior written disclosure to and consent of the Board, you may engage in other types of business or public activities. The Board may withdraw such consent, if the Board determines, in its sole discretion, that such activities compromise or threaten to compromise the Company’s or its Affiliates’ business interests or conflict with your duties to the Company or its Affiliates.

(c)    Non-Competition. During your employment by the Company, you will not, without the express written consent of the Company; directly or indirectly serve as an officer, director,

stockholder, employee, partner, proprietor, investor, joint venturer, associate, representative or consultant of any person or entity engaged in, or planning or preparing to engage in, business activity competitive with any line of business engaged in (or planned to be engaged in) by the Company or its Affiliates; provided, however, that you may purchase or otherwise acquire up to (but not more than) one percent (1%) of any class of securities of any enterprise (without participating in the activities of such enterprise) if such securities are listed on any national or regional securities exchange. In addition, you will be subject to certain restrictions (including restrictions continuing after your employment ends) under the terms of your Proprietary Information Agreement.

7.    At-Will Employment Relationship. Your employment relationship with the Company is employment at-will. Accordingly, you may terminate your employment with the Company at any time and for any reason whatsoever simply by notifying the Company; and the Company may terminate your employment at any time with or without cause or prior notice. In addition, the Company retains the discretion to modify your other employment terms from time to time, including but not limited to your position, duties, reporting relationship, work location, compensation (including base salary and bonus terms), and benefits.

8.    Dispute Resolution. To ensure the rapid and economical resolution of disputes that may arise in connection with your employment with and services for the Company and its Affiliates, you and the Company both agree that any and all disputes, claims, or causes of action, in law or equity, including but not limited to statutory claims, arising from or relating to the enforcement, breach, performance, or interpretation of this Agreement, your employment with and services for the Company and its Affiliates, or the termination of your employment with and services for the Company and its Affiliates, will be resolved pursuant to the Federal Arbitration Act, 9 U.S.C. §1-16, and to the fullest extent permitted by law, by final, binding and confidential arbitration conducted in San Diego, California by JAMS, Inc. (“JAMS”) or its successors by a single arbitrator. Both you and the Company acknowledge that by agreeing to this arbitration procedure, you each waive the right to resolve any such dispute through a trial by jury or judge or administrative proceeding.

Any such arbitration proceeding will be governed by JAMS’ then applicable rules and procedures for employment disputes, which can be found at http://www.jamsadr.com/rules-clauses/ and which will be provided to you upon request. In any such proceeding, the arbitrator shall: (a) have the authority to compel adequate discovery for the resolution of the dispute and to award such relief as would otherwise be permitted by law; and (b) issue a written arbitration decision including the arbitrator’s essential findings and conclusions and a statement of the award. You and the Company each shall be entitled to all rights and remedies that either would be entitled to pursue in a court of law. Nothing in this Agreement is intended to prevent either the Company or you from obtaining injunctive relief in court to prevent irreparable harm pending the conclusion of any such arbitration pursuant to applicable law. The Company shall pay all filing fees in excess of those which would be required if the dispute were decided in a court of law, and shall pay the arbitrator’s fees and any other fees or costs unique to arbitration. Any awards or orders in such arbitrations may be entered and enforced as judgments in the federal and state courts of any competent jurisdiction.

9.    General. This Agreement, along with Exhibit A, forms the complete and exclusive statement of your agreement with the Company regarding the subject matter hereof. It supersedes and replaces any other agreements or promises made to you by anyone concerning your employment terms, whether oral or written. This Agreement may not be amended or modified except by a written modification signed by you and a duly authorized officer of the Company, with the exception of those changes expressly reserved to the Company’s discretion in this Agreement. This Agreement is governed by the laws of the state of California, without reference to conflicts of law principles. If any provision of this Agreement shall be held invalid or unenforceable in any respect, such invalidity or unenforceability shall not affect the other

provisions of this Agreement, and such provision will be reformed, construed and enforced so as to render it valid and enforceable consistent with the general intent of the parties insofar as possible under applicable law. With respect to the enforcement of this Agreement, no waiver of any right hereunder shall be effective unless it is in writing. Any ambiguity in this Agreement shall not be construed against either party as the drafter. This Agreement may be executed in counterparts which shall be deemed to be part of one original, and facsimile signatures shall be equivalent to original signatures.

This offer is contingent on the successful completion of a background check. To confirm your terms of employment, please sign and date this letter and sign and date the Proprietary Information Agreement attached as Exhibit A, and return one signed copy of both documents to me by close of business on June 15, 2016. Please let me know if you have any questions.

Sincerely,

Exhibit A

PROPRIETARY INFORMATION AGREEMENT