Exhibit 10.66

uniQure N.V.

Restricted Share Unit Agreement

Granted Under 2014 Share Incentive Plan,

Amended and Restated effective as of June 16, 2021 (the “Amendment Date”)

General Terms and Conditions

1.Restricted Share Unit Grant. This Restricted Share Unit Grant Agreement (this “Agreement”) together with the Notice of Grant evidences the grant by the Company, on the Award Date to the Participant, of the number Restricted Share Units listed in the Notice of Grant, subject to the terms, restrictions and conditions set forth in this Agreement and the uniQure N.V. 2014 Share Incentive Plan, as amended and restated as of the Amendment Date (the “Plan”). Pursuant to this Agreement, the Company hereby grants to the Participant the right to receive ordinary shares of the Company (“Ordinary Shares”) in the amount and on the vesting schedule set forth on the Notice of Grant and on the terms set forth in this Agreement upon the satisfaction of the requirements of the vesting schedule set forth in Section 3 below. No Ordinary Shares shall be issued to the Participant on the Award Date. Unless otherwise defined herein, capitalized terms used in this Agreement shall have the meanings set forth in the Plan.

2.Shareholder Rights. Prior to the issuance, if any, of Ordinary Shares pursuant to the terms of this Agreement and the Plan, the Participant shall not (a) have any of the rights or privileges of a shareholder of the Company, including the right to vote the Ordinary Shares underlying the Restricted Share Units, (b) have the right to receive any dividends or other distributions, and (c) have any interest in any fund or specific assets of the Company by reason of this Agreement.

3.Vesting.

(a)The Restricted Share Units shall become vested in the amount set forth next to the respective Vesting Date set forth in the applicable Notice of Grant, if the Participant continues to be employed by the Company or a subsidiary of the Company employing the Participant (the “Employer”) from the Date of Grant until such date.

(b)If the Participant ceases to be an Eligible Participant for any reason prior to the date that the Restricted Share Units are vested, the Participant shall forfeit all unvested Restricted Share Units and the Participant will not have any rights with respect to any such unvested Restricted Share Units.

(c)Notwithstanding this Section 3, if a Reorganization Event (as defined in the Plan) occurs before the Restricted Share Units are fully vested and while the Participant is an Eligible Participant (as defined below), the Participant’s unvested Restricted Share Units shall automatically accelerate and become fully vested immediately prior to the Reorganization Event (except in cases where, following the Reorganization Event, securities (directly, or indirectly via one or more affiliated entities) possessing more that 50% of the total combined voting power of the survivor’s or acquiror’s outstanding securities are held by a person or persons who held securities possessing more than 50% of the total combined voting power of the Company’s outstanding securities immediately prior to the Reorganization Event (an “Internal Reorganization”)). An “Eligible Participant” means a Participant who is, and has been at all times since the Award Date, an employee, officer or a director of, or consultant or advisor (as such

terms are defined for purposes of Form S-8 under the Securities Act of 1933, as amended) to, the Company or any parent or subsidiary of the Company.

4.Issuance.

(a)The Restricted Share Units that become vested pursuant to Section 3 above shall be settled by the Company on the first business day following the date that the Restricted Share Units vest (the “Settlement Date”). Settlement will be made with respect to the Restricted Share Units in the form of Ordinary Shares, with each vested Restricted Share Unit equivalent to one Ordinary Share. In no event shall any fractional shares be issued.

(b)The obligation of the Company to deliver the Ordinary Shares to the Participant following the date that the Restricted Share Units vest in accordance with Section 3 above shall be subject to all applicable laws, rules, and regulations and such approvals by governmental agencies as may be deemed appropriate to comply with relevant securities laws and regulations.

5.Nonassignability of Ordinary Shares. The right to receive Ordinary Shares may not be sold, assigned, transferred, pledged or otherwise encumbered by the person to whom they are granted, either voluntarily or by operation of law, except by will or the laws of descent and distribution applicable to such Participant, except as permitted under the Plan or by the Supervisory Board or Board of Directors of the Company, as the case may be (the “Board”). Any attempt to sell, assign, transfer, pledge or otherwise encumber the right to receive Ordinary Shares contrary to the provisions of this Agreement and the Plan, and the levy of any execution, attachment or similar process upon the right to receive the shares, shall be null, void and without effect.

6.Provisions of the Plan. This grant is subject to the provisions of the Plan (including the provisions relating to amendments to the Plan), a copy of which will be furnished to the Participant.

7.Withholding. No Ordinary Shares will be issued unless and until the Participant pays to the Employer, or makes provision satisfactory to the Employer for payment of, any national, federal, state and local or other income, national insurance, social and employment taxes required by law to be withheld in respect of this grant. Without limiting the generality of the forgoing, on the Settlement Date, the Participant shall cause to be sold such number of Ordinary Shares as shall be required such that the proceeds thereof shall be sufficient to cover all amounts required to be withheld by the Company in respect of tax, and shall cause the proceeds thereof to be remitted to the Company.

8.No Employment or Other Rights. This grant shall not confer upon the Participant any right to be retained by or in the employ or service of the Employer and shall not interfere in any way with the right of the Employer to terminate the Participant’s employment or service at any time. The right of the Employer to terminate the Participant’s employment or service pursuant to the terms of the Participant’s employment agreement, if any, is specifically reserved.

9.Recoupment Policy. The Participant agrees that the Participant will be subject to any applicable clawback and recoupment policies, share trading policies and other policies that may be applicable to the Participant as an employee of the Employer, as in effect from time to time, whether or not approved before or after the Award Date.

10.Assignment by Company. The rights and protections of the Company hereunder shall extend to any successors or assigns of the Company and to the Company’s parents, subsidiaries, and affiliates. This Agreement may be assigned by the Company without the Participant’s consent.

11.Notice. Any notice to the Company provided for in this Agreement shall be addressed to the Head of Human Resources or the Chief Financial Officer at their respective corporate address at the Company, and any notice to the Participant shall be addressed to such Participant at the current address shown on the payroll of the Employer, or to such other address as the Participant may designate to the Employer in writing. Any notice shall be delivered by hand, sent by telecopy or enclosed in a properly sealed envelope addressed as stated above, registered and deposited with postage prepaid.

12.Nature of the Grant. In accepting the Restricted Share Units, the Participant acknowledges that:

(a)the Plan is established voluntarily by the Company, it provides for certain criteria in order to be eligible to receive an award, it is restricted in time, it is discretionary in nature and it may be modified, amended, suspended or terminated by the Company at any time, unless otherwise provided in the Plan and this Agreement;

(b)the grant of the Restricted Share Units is voluntary and occasional and does not create any contractual or other right to receive future grants, or benefits in lieu of grants, even if grants have been granted repeatedly in the past;

(c)all decisions with respect to future grants, if any, will be at the sole discretion of the Board;

(d)the Participant is voluntarily participating in the Plan;

(e)the Restricted Share Units are an extraordinary item that do not constitute compensation of any kind for services of any kind rendered to the Company or the Employer, and which is outside the scope of the Participant’s employment or consultancy agreement of his or her corporate mandate, if any;

(f)the Restricted Share Units are not part of normal or expected compensation or salary for any purposes, including, but not limited to, calculation of any severance, resignation, termination, redundancy, end of service payments, bonuses, long-service awards, pension, retirement or welfare benefits or similar payments and in no event should be considered as compensation for, or relating in any way, to past services for the Company or the Employer;

(g)in the event that the Participant is not an employee of the Company, the Restricted Share Units and the Participant’s participation in the Plan will not be interpreted to form an employment or service contract or relationship with the Company;

(h)the future value of the underlying Ordinary Shares is unknown and cannot be predicted with certainty; if the Participant’s Restricted Share Units never vest, the Participant will not be eligible to receive any Ordinary Shares; and

(i)in consideration of the Restricted Share Units, no claim or entitlement to compensation or damages shall arise from termination of the Restricted Share Units or from any decrease in value of the Restricted Share Units or Ordinary Shares that may be or have been acquired resulting from

termination of the Participant’s employment, consultancy or corporate mandate by or with the Company or the Employer (for any reason whatsoever and whether or not in breach of contract or local laws) and the Participant irrevocably releases the Company and the Employer from any such claim that may arise.

13.Data Privacy. The Participant hereby explicitly and unambiguously consents to the collection, use and transfer, in electronic or other form, of his or her personal data as described in this agreement by and among, as applicable, his or her Employer or contracting party and the Company for the exclusive purpose of implementing, administering and managing his or her participation in the Plan.

The Participant understands that the Company holds certain personal information about him or her, including, but not limited to, his or her name, home address and telephone number, work location and phone number, date of birth, hire date, details of all Restricted Share Units or any other entitlement to Ordinary Shares awarded, cancelled, exercised, vested, unvested or outstanding in the Participant’s favor, for the purpose of implementing, administering and managing the Plan (“Personal Data”). The Participant understands that Personal Data may be transferred to any third parties assisting in the implementation, administration and management of the Plan, that these recipients may be located in the Participant’s country or elsewhere and that the recipient’s country may have different data privacy laws and protections than the Participant’s country. The Participant understands that he or she may request a list with the names and addresses of any potential recipients of the Personal Data by contacting his or her local human resources representative. The Participant authorizes the recipients to receive, possess, use, retain and transfer the Personal Data, in electronic or other form, for the purposes of implementing, administering and managing his or her participation in the Plan, including any requisite transfer of such Personal Data as may be required to a broker or other third party with whom the Participant may elect to deposit any Ordinary Shares acquired pursuant to the Restricted Share Units. The Participant understands that Personal Data will be held only as long as is necessary to implement, administer and manage his or her participation in the Plan. The Participant understands that he or she may, at any time, view Personal Data, request additional information about the storage and processing of Personal Data, require any necessary amendments to Personal Data or refuse or withdraw the consents herein, in any case without cost, by contacting in writing his or her local human resources representative. The Participant understands, however, that refusing or withdrawing his or her consent may affect his or her ability to participate in the Plan. For more information on the consequences of Participant’s refusal to consent or withdrawal of consent, the Participant understands that he or she may contact his or her local human resources representative.

14.Section 409A. This Agreement is not intended to constitute or result in deferred compensation subject to the requirements of section 409A of the Code. However, to the extent any amount payable under this Agreement is subsequently determined to constitute deferred compensation subject to the requirements of section 409A of the Code, this Agreement shall be administered in accordance with the requirements of section 409A of the Code. In such case, distributions shall only be made on an event and in a manner permitted by section 409A of the Code, including the six-month delay for specified employees consistent with Section 11(g) of the Plan, if applicable. To the extent that any provision of this Agreement would cause a conflict with the requirements of section 409A of the Code, or would cause the administration of this Agreement to fail to satisfy the requirements of section 409A of the Code, such provision shall be deemed null and void to the extent permitted by applicable law. In no event shall the Participant, directly or indirectly, designate the calendar year of redemption. This Agreement may be amended without the consent of the Participant in any respect deemed by the Board to be necessary in order to preserve compliance with Section 409A of the Code. Each distribution

pursuant to this Agreement shall be deemed a separate payment for purposes of Section 409A of the Code.

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Participant must sign this agreement within 90 days of the Vest Date as set forth on the applicable Notice of Grant by clicking on the button “I Accept”. The plan agreement will then be stored under the “Grants & Awards” menu in Computershare.