Exhibit 5.1

16 February 2018

Board of Directors

Allergan plc

Clonshaugh Business and Technology Park

Coolock

Dublin 17

Ireland

Re: Allergan plc – Form S-3 Registration Statement

Dear Sirs

1. Basis of Opinion

1.1 We are acting as Irish counsel to Allergan plc, a public company limited by shares, incorporated under the laws of Ireland, company number 527629, with its registered office at Clonshaugh Business and Technology Park, Coolock, Dublin 17, Ireland (the “Company”) in connection with the registration statement on Form S-3 (the “Registration Statement”) to be filed with the United States Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended (the “Securities Act”) on or around 16 February 2018 (the “Registration Statement”). We refer, in particular, to the ordinary shares of US$0.0001 par value and the serial preferred shares of US$0.0001 par value of the Company (the “Shares”) that may be issued pursuant to the Registration Statement.

1.2 This Opinion is confined to and given in all respects on the basis of the laws of Ireland (meaning Ireland exclusive of Northern Ireland) in force as at the date hereof as currently applied by the courts of Ireland. We have made no investigation of, and we express no opinion as to the laws of, any other jurisdiction or the effect thereof. This Opinion speaks only as of its date.

1.3 This Opinion is also strictly confined to the matters expressly stated herein at paragraph 2 below and is not to be read as extending by implication or otherwise to any other matter.

1.4 As Irish counsel to the Company in connection with the registration of the Shares, we have examined:

(a) the documents listed in the schedule (the “Schedule”) to this opinion (the “Documents”);

(b) the searches listed at paragraph 1.6 below; and

(c) such other documents and records as we have deemed necessary to enable us to render the opinions set forth below.

1.5 In giving this Opinion, we have examined and relied on copies of the Documents sent to us by e-mail in pdf or other electronic format.

1.6 For the purpose of giving this Opinion, we have caused to be made the following legal searches against the Company on 16 February 2018:

(a) on the file of the Company maintained by the Irish Registrar of Companies in Dublin for returns of allotments, special resolutions amending the memorandum and articles of association of the Company and notice of the appointment of directors and secretary of the Company and for the appointment of any receiver, examiner or liquidator;

(b) in the Judgments Office of the High Court for unsatisfied judgments, orders, decrees and the like for the twelve years immediately preceding the date of the search; and

(c) in the Central Office of the High Court in Dublin for any proceedings and petitions filed in respect of the Company.

2. Opinion

Subject to the assumptions set out in this Opinion and to any matters not disclosed to us, we are of the opinion that:

2.1 the Company is a public company limited by shares, is duly incorporated and validly existing under the laws of Ireland and has the requisite corporate authority to issue the Shares; and

2.2 when the Shares are issued and allotted pursuant to duly adopted resolutions of the board of directors of the Company (including resolutions duly adopted by the board appointing a committee thereof for purposes of exercising the Company’s powers in respect of the allotment and issue of the Shares), the Shares shall be validly issued, fully paid up and non-assessable (which term means that no further sums are required to be paid by the holders thereof in connection with the issue of such Shares).

3. Assumptions

For the purpose of giving this Opinion, we assume the following without any responsibility on our part if any assumption proves to have been untrue as we have not verified independently any assumption:

3.1 Registration Statement

(a) that, when filed with the SEC, the Registration Statement will not differ in any material respect from the drafts that we have examined;

(b) that any Shares issued under the Registration Statement will be in consideration of the receipt by the Company prior to the issue of the Shares pursuant thereto of cash at least equal to the par value of such Shares;

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(c) that the filing of the Registration Statement with the SEC has been authorised by all necessary actions under all applicable laws other than Irish law;

(d) that, at the time of issue of the Shares, the authority of the Company and the directors of the Company to allot and issue the Shares, as provided for in the articles of association of the Company and the Companies Act 2014 of Ireland (as amended) (the “Companies Act”), is in full force and effect;

(e) that the Company will continue to renew its authority to allot and issue the Shares in accordance with the terms and conditions set out in the articles of association of the Company and the Companies Act and that, where such authority has not been renewed, the Company will not allot and issue the Shares after such authority has expired;

(f) that, at the time of issue of the Shares, the Company will have sufficient authorised but unissued share capital to issue the required number of Shares;

(g) that any issue of Shares will be in compliance with the Companies Act, the Irish Takeover Panel Act 1997, Takeover Rules 2013, and all other applicable Irish company, takeover, securities, prospectus, market abuse and insider dealing laws and other rules and regulations;

(h) that, as at the time of issuance of the Shares, such issuance shall not be in contravention or breach of any agreement, undertaking, arrangement, deed or covenant affecting the Company or to which the Company is a party or otherwise bound or subject;

3.2 Authenticity and Bona Fides

(a) the completeness and authenticity of all Documents submitted to us as originals or copies of originals (and in the case of copies, conformity to the originals of such copies), the genuineness of all signatories, stamps and seals thereon;

(b) where incomplete Documents have been submitted to us or signature pages only have been supplied to us for the purposes of issuing this Opinion, that the originals of such Documents correspond in all respects with the last draft of the complete Documents submitted to us;

(c) that the Documents will be executed in a form and content having no material difference to the drafts provided to us, will be delivered by the parties thereto, and that the terms thereof will be observed and performed by the parties thereto;

(d) that the copies produced to us of minutes of meetings and/or of written resolutions correctly record the proceedings at such meetings and/or the subject matter which they purport to record and that any meetings referred to in such copies were duly convened, duly quorate and held, that those present at any such meetings were entitled to attend and vote at the meeting and acted bona fide throughout and that no further resolutions have been passed or other action taken which would or might alter the effectiveness thereof;

(e) that there is, at the relevant time of the allotment and issue of the Shares, no matter affecting the authority of the directors to issue and allot the Shares, not disclosed by the memorandum and articles of association of the Company or the resolutions produced to us, which would have any adverse implications in relation to the opinions expressed in this Opinion;

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(f) that the memorandum and articles of association effective as of 5 May 2016 are the current memorandum and articles of association of the Company, are up to date and have not been amended or superseded and that there are no other terms governing the Shares other than those set out in the memorandum and articles of association of the Company;

3.3 Accuracy of searches and warranties

(a) the accuracy and completeness of the information disclosed in the Searches and that such information has not since the time of such search or enquiry been altered. It should be noted that searches at the Companies Registration Office, Dublin, do not necessarily reveal whether or not a prior charge has been created or a resolution has been passed or a petition presented or any other action taken for the winding-up of or the appointment of a receiver or an examiner to the Company;

(b) that there has been no alteration in the status or condition of the Company as disclosed by the Searches;

3.4 Solvency and Insolvency

(a) that:

(i) the Company will not be unable to pay its debts within the meaning of Sections 509(3) and 570 of the Companies Act or any analogous provision under any applicable laws immediately after the filing of the Registration Statement with the SEC;

(ii) the Company will not as a consequence of doing any act or thing which the Registration Statement contemplates, permits or requires any relevant party to do, be unable to pay its debts within the meaning of such Sections or any analogous provisions under any applicable laws;

(iii) no liquidator, receiver or examiner or other similar or analogous officer has been appointed in relation to the Company or any of its assets or undertaking; and

(iv) no petition for the making of a winding-up order or the appointment of any examiner or any similar officer or any analogous procedure has been presented in relation to the Company; and

3.5 General

(a) that no proceedings have been instituted or injunction granted against the Company to restrain it from issuing the Shares and the issue of any Shares would not be contrary to any state, governmental, court, state or quasi-governmental agency, licensing authority, local or municipal governmental body or regulatory authority’s order, direction, guideline, recommendation, decision, licence or requirement.

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4. Disclosure

This Opinion is addressed to you in connection with the registration of the Shares with the SEC. We hereby consent to the inclusion of this Opinion as an exhibit to the Registration Statement to be filed with the SEC and any amendments thereto. We also hereby consent to the reference to our firm under the caption “Legal Matters” in the Registration Statement. In giving this consent, we do not thereby admit that we are in a category of person whose consent is required under Section 7 of the Securities Act.

The opinion is governed by and is to be construed in accordance with the laws of Ireland as interpreted by the courts of Ireland at the date hereof.

Yours faithfully

/s/ Arthur Cox

ARTHUR COX

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SCHEDULE

Documents

1. A copy of the form of the Registration Statement to be filed by the Company with the SEC.

2. A copy of the resolutions of the board of directors of the Company dated 8 February 2018.

5. A corporate certificate of the secretary of the Company dated 16 February 2018.

3. A copy of the memorandum and articles of association of the Company as amended and restated by special resolution on 5 May 2016.

4. A copy of the certificate of incorporation of the Company dated 16 May 2013.

5. A copy of the certificate of incorporation on change of name of the Company dated 17 May 2013.

6. A copy of the certificate of incorporation on re-registration as a public limited company of the Company dated 20 September 2013.

7. A copy of the certificate of incorporation on change of name of the Company dated 16 June 2015.

8. A letter of status from the Irish Companies Registration Office dated 16 February 2018.

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