Executive Employment and Transition Agreement, dated May 11, 2022, by and among Horizon Therapeutics Public Limited Company, Horizon Therapeutics USA, Inc. and Paul W. Hoelscher

Exhibit 10.4

EXECUTIVE EMPLOYMENT AND TRANSITION AGREEMENT

This Executive Employment and Transition Agreement (this “Agreement”) is entered into on May 11, 2022, by and among Horizon Therapeutics plc, an Irish Public Limited Company, and its wholly owned subsidiary, Horizon Therapeutics USA, Inc., a Delaware corporation, having a principal place of business at 1 Horizon Way, Deerfield, Illinois 60015 (hereinafter referred to together as the “Company”) and Paul W. Hoelscher (the “Executive”), and replaces and supersedes that certain Executive Employment Agreement dated June 17, 2014 and that certain First Amendment to Executive Employment Agreement dated May 4, 2017 (collectively the “Prior Agreements”), by and between Horizon Therapeutics USA, Inc. and the Executive. This Agreement shall become effective on the “Effective Date” specified in Section 10 below.

RECITALS

WHEREAS, the Company and the Executive have previously entered into the Prior Agreements, the Executive has notified the Company of his intention to retire on May 16, 2022 and the Executive has provided exceptional service pursuant to the Prior Agreements that has materially enhanced the performance and value of the Company;

WHEREAS, the Prior Agreements may be amended with the written agreement of the Company and the Executive;

WHEREAS, the Company and the Executive desire to provide continuity and efficiency in connection with the Company’s appointment of a new Chief Financial Officer effective with the Executive’s retirement, and provide for transition and post-employment advisor services by the Executive; and

WHEREAS, the Company and the Executive desire to supersede and replace the Prior Agreements with this Agreement.

AGREEMENT

NOW, THEREFORE, in consideration of the foregoing and the promises and covenants contained herein, and for other good and valuable consideration, the receipt of which is hereby acknowledged, the parties hereto agree as follows:

1. TRANSITION PERIOD. The Executive shall remain employed as a full-time employee and Executive Vice President and Chief Financial Officer of the Company (“CFO”) through May 16, 2022 (the “Transition Period”). During the Transition Period the Executive shall continue to receive his current base salary and the Executive and his eligible dependents, if applicable, shall remain enrolled in all Company-sponsored benefit programs in which he (or they) were enrolled as of the Effective Date. During the Transition Period, the Executive shall work collaboratively with Aaron Cox, Executive Vice President, Finance, on all matters relating to Aaron Cox’s transition into the role of CFO effective as of May 16, 2022, along with such additional duties consistent with the role of CFO as may be required of the Executive. The Executive’s employment as CFO and with the Company shall terminate effective May 16, 2022 (the “Retirement Date”). Following the Retirement Date, the Executive shall no longer have any: (i) responsibilities as the Company’s CFO, (ii) responsibility to sign the Company’s future filings with the Securities and

Exchange Commission, or (iii) other authority or responsibilities as an officer of the Company or any of its subsidiaries. Effective as of the Retirement Date, the Executive also hereby resigns from any director, manager or similar roles on governing bodies of the Company’s subsidiaries.

2. RETIREMENT BENEFITS.

(a) Prorated 2022 Annual Bonus. Provided that the Executive has timely executed, returned, and does not revoke this Agreement, and complies with Executive’s contractual and legal obligations to the Company (including without limitation those specified in Sections 1, 5, 6, and 7 of this Agreement and the Confidentiality Agreement (as defined below)), then notwithstanding the requirement that Executive remain employed on the date such bonus is awarded to be eligible for such bonus, the Company will pay Executive an amount equal to the product of (i) the annual discretionary performance bonus that Executive would have been entitled to receive for calendar year 2022, subject to a target of 70% of the Executive’s annual base salary and the Company’s and Executive’s achievement of performance milestones as established by the Company’s Board of Directors or the compensation committee thereof, and (ii) a fraction, the numerator of which is the number of days Executive was continuously employed by the Company for calendar year 2022 and the denominator of which is the number of days in such year (the “Prorated Bonus”). The Prorated Bonus will be paid to Executive, subject to standard payroll deductions and withholdings, in a lump sum at the time such annual discretionary bonuses are paid out to similarly situated employees of the Company (but in no event later than March 15, 2023), provided that this Agreement has become effective by its terms as of such date.

(b) COBRA Subsidy. If the Executive timely elects continued coverage under COBRA, the Company will continue to pay the same percentage of the Executive’s COBRA health insurance premium as the percentage of health insurance premiums that it paid during the Executive’s employment (the “COBRA Subsidy”), including any amounts that the Company paid for benefits to the qualifying family members of the Executive, following the Retirement Date until the earlier of either (i) the date on which the Executive begins full-time employment with another company or business entity which offers comparable health insurance coverage to the Executive, or (ii) December 31, 2022 (such period, the “COBRA Payment Period”). Notwithstanding the foregoing, if the Company determines, in its sole discretion, that the Company cannot provide the COBRA Subsidy without potentially violating the nondiscrimination requirements under Internal Revenue Code Section 105(h) or the Executive incurring additional income tax liability, the Company shall in lieu thereof pay the Executive a taxable cash amount, which payment shall be made regardless of whether the Executive or his qualifying family members elect COBRA continuation coverage (the “Health Care Benefit Payment”), and which the Executive may, but is not obligated to, use to pay for medical expenses, including COBRA premiums. The Health Care Benefit Payment shall be paid in monthly installments. The Health Care Benefit Payment shall be equal to the amount of the COBRA Subsidy (which amount shall be calculated based on the premium for the first month of coverage), and shall be paid until the date the COBRA Payment Period expires or otherwise would have expired if the Executive does not elect continued coverage under COBRA.

(c) Financial Advisory Services. The Company will pay for, or reimburse the Executive for, the fees associated with the Executive’s continued use of personal financial

advisory services provided by JMG Financial Group through December 31, 2023, up to $10,000.00 per year.

3. PART-TIME ADVISOR ROLE. From the date immediately following the Retirement Date until terminated as specified herein, the Executive shall serve as a part-time advisor to the Company, providing services consistent with his expertise and experience as a chief financial officer (the “Part-time Advisor Period”). For purposes of this Section 3, “part-time” shall mean the Executive shall be available to the Company to provide such services as may be requested by the Company (a) for up to twenty (20) hours per week from the date immediately following the Retirement Date through May 16, 2023 and (b) for up to 5 hours per month from May 17, 2023 until the Part-time Advisor Period is terminated by either party. During the Part-time Advisor Period, the Company shall pay to the Executive compensation at the rate of (x) $27,500 per month through May 16, 2023 and (y) $5,000 per year after May 16, 2023. Such compensation shall not be subject to any tax or other withholding and shall be reported on Form 1099 and shall be paid to the Executive in arrears on the first business day of each calendar month. During the Part-time Advisor Period, the Company will not make deductions from any amounts payable to the Executive for taxes or social securities. Payment of all taxes and social securities due on any amounts paid to the Executive for services provided during the Part-time Advisor Period shall be the sole responsibility of the Executive. Upon the Executive filing his Form 1040 Individual U.S. Federal Income Tax return as it relates to the Part-time Advisor Period in any particular tax year, the Executive shall provide the Company with a signed Form 4669, “Statement of Payments Received” attesting that the Executive reported the amounts received from the Company for services performed during the Part-time Advisor Period in such tax year as taxable income.

During the Part-time Advisor Period, the Company will also reimburse the Executive for reasonable and documented out-of-pocket costs and expenses actually incurred in connection with providing the services requested by the Company, including travel costs and other similar expenses, subject to and in accordance with the Company’s travel and expense policies in effect from time to time.

As additional consideration, the Company will consider the Executive’s change of status from an employee to an advisor, and the Executive’s service to the Company during the Part-Time Advisor Period, as service as a “Consultant” and to constitute “Continuous Service” for purposes of the Company’s Amended and Restated 2014 Equity Incentive Plan, the Company’s Amended and Restated 2018 Equity Incentive Plan and the Company’s Amended and Restated 2020 Equity Incentive Plan (together, each as amended from time to time, the “Equity Plans”), and, therefore, each of the Executive’s equity awards granted under any of the Equity Plans (each, an “Equity Award”), to the extent outstanding as of the Retirement Date, will continue to vest in accordance with their terms during the Part-time Advisor Period; provided that any such Equity Awards that are “incentive stock options” under Section 422 of the Internal Revenue Code of 1986, as amended (the “Code”) shall cease to be “incentive stock options” following the three (3) month anniversary of the Retirement Date, or earlier pursuant to the Extended Exercise Period Amendment (as defined below), if applicable. Except as provided herein, all terms, conditions and limitations applicable to the Equity Awards will continue to be subject to and governed and controlled by the Equity Plans and the Executive’s applicable grant documents (the “Equity Documents”).

The Executive’s relationship with the Company during the Part-time Advisor Period will be that of an independent contractor, and nothing in this Agreement is intended to, or should be construed to, create a partnership, agency, joint venture or employment relationship after the Retirement Date. The Executive acknowledges and agrees that the advisor relationship with the Company during the Part-time Advisor Period will not be subject to the Fair Labor Standards Act or other laws or regulations governing employment relationships. During the Part-time Advisor Period, the Executive will have no authority to bind the Company to any contractual obligations, whether written, oral or implied, except with the authorization of the Company’s Chief Executive Officer or Chief Financial Officer. Further, the Executive agrees not to represent or purport to represent the Company to any third party (including but not limited to investors, analysts, business partners or vendors), unless authorized by the Company’s Chief Executive Officer or Chief Financial Officer to do so.

Without waiving any other rights or remedies, the Company has the right to immediately terminate the Part-time Advisor Period without cost or liability, except as provided herein, after May 16, 2023, upon providing written notice of such termination to the Executive. Without waiving any other rights or remedies, the Executive has the right to immediately terminate the Part-time Advisor Period without cost or liability at any time for any reason upon providing written notice of such termination to the Company. If the Company terminates the Part-time Advisor Period after May 16, 2023 or if the Part-time Advisor Period is terminated due to the Executive’s death, then notwithstanding anything in the Equity Plans or Equity Documents to the contrary, with respect to each Equity Award that is outstanding as of the date of such termination:

4. NO OTHER COMPENSATION OR BENEFITS. The Executive acknowledges that, except as expressly provided in this Agreement, Executive has not earned, will not earn after the Retirement Date, and will not receive from the Company or any of its affiliates any of the benefits that the Company may make available to its employees or any additional compensation (including base salary, bonus, retention payments, incentive compensation, commissions, or equity), severance, or benefits prior to, on, or after the Retirement Date.

5. RETURN OF COMPANY PROPERTY. Upon the Retirement Date (or earlier if requested by the Company), and subject to the last sentence of this Section 5, the Executive must immediately return to the Company all Company documents (and all copies thereof) and other Company property that the Executive has in the Executive’s possession or control, including but not limited to any materials of any kind that contain or embody any proprietary or confidential information of the Company or its affiliates (and all reproductions thereof in whole or in part). The Executive further represents that the Executive will make a diligent search to locate any such documents, property and information. In addition, if the Executive has used any personally owned computer, server, e-mail system, mobile phone, or portable electronic device (e.g., iPhone, iPad, Android) (collectively, “Personal Systems”) to receive, store, prepare or transmit any Company or affiliate confidential or proprietary data, materials or information, then the Executive must immediately provide the Company with a computer-useable copy of all such information and then permanently delete and expunge all such Company or affiliate confidential or proprietary information from such Personal Systems without retaining any copy or reproduction in any form. During the Part-time Advisor Period, the Company may permit the Executive to receive and/or use certain documents, equipment, and/or information reasonably necessary to perform the advisor services, all of which the Executive shall return to the Company by the last day of the Part-time Advisor Period, or earlier upon the Company’s request, without retaining any copies or embodiments (in whole or in part).

6. CONFIDENTIAL INFORMATION. The Executive acknowledges his continuing obligations under his previously executed Confidential Information and Invention Assignment Agreement dated June 23, 2014 (the “Confidentiality Agreement”). Pursuant to the Confidentiality Agreement, the Executive understands that among other things, the Executive must not use or disclose any confidential or proprietary information of the Company and the Executive must immediately return all Company property and documents (including all embodiments of proprietary information) and all copies thereof in the Executive’s possession or control. The Executive understands and agrees that the Executive’s right to the payments and other benefits the Executive is receiving in exchange for the Executive’s agreement to the terms of this Agreement is contingent upon the Executive’s continued compliance with the Executive’s Confidentiality Agreement. Notwithstanding the foregoing nondisclosure obligations, pursuant to 18 U.S.C. Section 1833(b), the Executive will not be held criminally or civilly liable under any federal or state trade secret law for the disclosure of a trade secret that is made: (i) in confidence to a federal, state, or local government official, either directly or indirectly, or to an attorney, and solely for the purpose of reporting or investigating a suspected violation of law; or (ii) in a complaint or other document filed in a lawsuit or other proceeding, if such filing is made under seal.

7. NON-COMPETITION/NON-SOLICITATION AGREEMENT. During the time the Executive performs services or receives any compensation or benefits pursuant to this Agreement, the Executive i) will not, without the prior written consent of the Company, participate as an owner (which shall not include ownership of less than 2% of the stock of a publicly-traded company),

employee, officer, director, promoter, or consultant in a business that is directly competitive with the Company; ii) the Executive will not request, induce or advise any vendors, existing or potential corporate partners or investors, and/or customers of the Company to withdraw, curtail, limit, reduce, or cancel their business or business relationship(s) with the Company; and iii) will not hire any employees, consultants, contractors or representatives of the Company (or those of any of its affiliates), nor induce or attempt to induce, or assist any other person or entity to (including without limitation by providing such person or entity any information regarding the Company’s business or employees) induce or attempt to induce such employees, consultants, contractors or representatives to stop working for, contracting with or representing the Company or any of its affiliates.

8. RELEASE. In exchange for the consideration provided to the Executive by this Agreement that the Executive is not otherwise entitled to receive, the Executive hereby generally and completely releases the Company and its past and present directors, officers, employees, shareholders, members, partners, agents, attorneys, predecessors, successors, parent and subsidiary entities, insurers, affiliates, and assigns from any and all claims, liabilities and obligations, both known and unknown, that arise out of or are in any way related to events, acts, conduct, or omissions occurring prior to the Executive signing this Agreement. This general release includes, but is not limited to: (1) all claims arising out of or in any way related to the Executive’s employment or service relationship with the Company or the separation of that employment or service relationship; (2) all claims related to the Executive’s compensation or benefits from the Company (except compensation and benefits expressly provided in this Agreement), including, but not limited to, salary, bonuses, commissions, vacation pay, expense reimbursements, severance pay, fringe benefits, stock, stock options, restricted stock units, performance stock units, or any other ownership interests in the Company; (3) all claims for breach of contract, wrongful termination, and breach of the implied covenant of good faith and fair dealing; (4) all tort claims, including, but not limited to, claims for fraud, defamation, emotional distress, and discharge in violation of public policy; and (5) all federal, state, and local statutory claims, including, but not limited to, claims for discrimination, harassment, retaliation, attorneys’ fees, or other claims arising under the federal Civil Rights Act of 1964 (as amended), the federal Americans with Disabilities Act of 1990, the federal Age Discrimination in Employment Act of 1967 (as amended) (“ADEA”), the Illinois Human Rights Act, the Illinois Equal Pay Act, the Illinois Religious Freedom Restoration Act, the Illinois Genetic Information Privacy Act, the Illinois Employment Contract Act, the Illinois Labor Dispute Act, the Illinois Victims’ Economic Security and Safety Act, the Cook County Human Rights Ordinance, and the Chicago Human Rights Ordinance (collectively, the “Released Claims”).

9. EXCLUDED CLAIMS AND PROTECTED RIGHTS. Notwithstanding the foregoing, the following are not included in the Released Claims: (a) any rights or claims for indemnification the Executive may have pursuant to any written indemnification agreement with the Company or any of its subsidiaries to which the Executive is a party, the charter, bylaws, or operating agreements of the Company, or under applicable law; (b) any rights to participate in the Horizon Therapeutics Retiree Medical Plan; (c) as of the Retirement Date, all earned but unpaid base salary, any earned but unpaid discretionary bonuses for any prior period at such time as bonuses would have been paid if the Executive remained employed, all accrued but unpaid business expenses, and all accrued but unused vacation time earned through the Retirement Date at the rate in effect at such date; (d) any rights to Company matching contributions based on the Executive’s contributions to Company-sponsored retirement and deferred compensation plans through the

Retirement Date; (e) any rights to contributions by the Executive to the Company’s 2020 Employee Share Purchase Plan that are otherwise due to be returned to the Executive as a result of termination of employment under the terms of such plan and related offering documents; (f) any rights to tax gross-up payments associated with the value of personal benefits provided to the Executive through the Retirement Date in accordance with the Company’s standard practices; (g) any rights that are not waivable as a matter of law; or (h) any claims arising from the breach of this Agreement (the “Excluded Claims”). In addition, nothing in this Agreement prevents Executive from filing a charge or complaint with the Equal Employment Opportunity Commission, the National Labor Relations Board, the Occupational Safety and Health Administration, the Securities and Exchange Commission or any other federal, state or local governmental agency or commission (collectively, the “Government Agencies”). This Agreement does not limit the Executive’s ability to communicate with any Government Agencies or otherwise participate in any investigation or proceeding that may be conducted by any Government Agencies. While this Agreement does not limit the Executive’s right to receive an award for information provided to the Securities and Exchange Commission, the Executive understands and agrees that, to maximum extent permitted by law, the Executive is otherwise waiving any and all rights the Executive may have to individual relief based on any claims that the Executive has released and any rights the Executive has waived by signing this Agreement. The Executive hereby represents and warrants that, other than the Excluded Claims, the Executive is not aware of any claims the Executive has or might have against any of the Released Parties that are not included in the Released Claims.

10. ADEA WAIVER. The Executive hereby knowingly and voluntarily waives and releases any rights the Executive may have under the ADEA (as defined above). The Executive also acknowledges that the consideration given for the Executive’s releases in this Agreement is in addition to anything of value to which the Executive was already entitled. The Executive is advised by this writing that: (a) the Executive’s waiver and release does not apply to any claims that may arise after the Executive signs this Agreement; (b) the Executive should consult with an attorney prior to executing this release; (c) the Executive has twenty-one (21) days within which to consider this release (although the Executive may choose to voluntarily execute this release earlier); (d) the Executive has seven (7) days following the execution of this release to revoke this Agreement; and (e) this Agreement will not be effective until the eighth day after the Executive signs this Agreement, provided that the Executive has not earlier revoked this Agreement (the “Effective Date”). The Executive will not be entitled to receive any of the benefits specified by this Agreement unless and until it becomes effective.

11. ENTIRE AGREEMENT. This Agreement, including Executive’s Confidentiality Agreement, constitutes the complete, final and exclusive embodiment of the entire agreement between the Executive and the Company with regard to this subject matter. It is entered into without reliance on any promise or representation, written or oral, other than those expressly contained herein, and it supersedes any other such promises, warranties or representations, including without limitation, the Prior Agreements. The Executive agrees and acknowledges that there are no circumstances as of the date of this Agreement that constitute, and nothing contemplated in this Agreement shall be deemed for any purpose to be or to create, an involuntary termination without Cause or a Good Reason resignation right, including for purposes of Section 4 of the Prior Agreements, or any other severance or change in control plan, agreement or policy maintained by the Company. The Executive further hereby expressly waives any claim or right the Executive may have as of the date of this Agreement (if any) to assert that this Agreement, or any

other condition or occurrence, forms the basis for a without Cause termination or Good Reason resignation for any purpose, including for purposes of Section 4 of the Prior Agreements, or any other severance or change in control plan, agreement or policy maintained by the Company.

12. SUCCESSORS AND ASSIGNS. This Agreement will bind the heirs, personal representatives, successors and assigns of both the Executive and the Company, and inure to the benefit of both the Executive and the Company, their heirs, successors and assigns. The Executive may not assign any of the Executive’s duties hereunder and the Executive may not assign any of the Executive’s rights hereunder without the written consent of the Company.

13. APPLICABLE LAW. This Agreement shall be deemed to have been entered into and shall be construed and enforced in accordance with the laws of the State of Illinois as applied to contracts made and to be performed entirely within Illinois.

14. SEVERABILITY. If a court or arbitrator of competent jurisdiction determines that any term or provision of this Agreement is invalid or unenforceable, in whole or in part, the remaining terms and provisions hereof shall be unimpaired. Such court or arbitrator will have the authority to modify or replace the invalid or unenforceable term or provision with a valid and enforceable term or provision that most accurately represents the parties’ intention with respect to the invalid or unenforceable term or provision.

15. MODIFICATION; WAIVER; INTERPRETATION. This Agreement may not be modified or amended except in a writing signed by both the Executive and the Chief Executive Officer of the Company. The failure to enforce any breach of this Agreement shall not be deemed to be a waiver of any other or subsequent breach. For purposes of construing this Agreement, any ambiguities shall not be construed against either party as the drafter.

16. INDEMNIFICATION. The Executive will indemnify and save harmless the Company from any loss incurred directly or indirectly by reason of the falsity or inaccuracy of any representation made herein.

17. SECTION HEADINGS. The section and paragraph headings contained in this Agreement are for reference purposes only and shall not affect in any way the meaning or interpretation of this Agreement.

18. COUNTERPARTS; SIGNATURES. This Agreement may be executed in two counterparts, each of which shall be deemed an original, all of which together shall constitute one and the same instrument. A photocopy of this executed Agreement shall be as valid, binding, and effective as the original Agreement. This Agreement may be delivered and executed via facsimile, electronic mail (including pdf or any electronic signature complying with the U.S. federal ESIGN Act of 2000, Uniform Electronic Transactions Act or other applicable law) or other transmission method and shall be deemed to have been duly and validly delivered and executed and be valid and effective for all purposes.

IN WITNESS WHEREOF, the parties have executed this Executive Employment and Transition Agreement as of the date first written above.