Buckley's career progressed with starring roles in the HBO miniseries Chernobyl (2019), I'm Thinking of Ending Things (2020), season four of Fargo (2020), The Lost Daughter (2021), Men (2022) and Women Talking (2022).

Buckley's portrayal of Sally Bowles in a 2021 West End theatre revival of Cabaret won her the Laurence Olivier Award for Best Actress in a Musical.

She attended summer workshops with the Association of Irish Musical Societies (AIMS) to improve her singing and acting, and it was here that she was recognised as a talented actress and encouraged to apply for drama school in London.

[5] Buckley began her career as a contestant on I'd Do Anything, a talent show centred on the search for a new, unknown lead to play Nancy in the 2009 West End revival of the British musical Oliver!.

[citation needed] On 14 September 2008, Buckley performed at an outdoor concert in celebration of Andrew Lloyd Webber's birthday in Hyde Park, London.

[5] During Shakespeare's Globe's 2013 summer season, she played Miranda in The Tempest, and singer Arabella Hunt and Kate in Samuel Adamson's Gabriel.

[16][17] In September 2013, Buckley appeared opposite Jude Law in Michael Grandage's West End production of Henry V at the Noël Coward Theatre.

After an episodic appearance in the detective drama series Endeavour, Buckley portrayed Marya Bolkonskaya in BBC's new dramatisation of War and Peace (2016).

[23] She also starred as Honor Martin in BBC One's drama The Last Post (2017), and as Marian Halcombe in the five-part television adaptation of Wilkie Collins' novel The Woman in White (2018).

The same year, Buckley had a lead role in the fourth season of the FX black comedy crime drama Fargo, where she played nurse Oraetta Mayflower.

[29][30][31][32] In 2021, Buckley starred as the younger version of Leda Caruso in Maggie Gyllenhaal's feature directorial debut The Lost Daughter, with Olivia Colman portraying the character's older counterpart.

[34] The production opened to rave reviews in the West End in November 2021,[35][36] winning Best Musical Revival and Buckley's own as Best Actress at the 2022 Olivier Awards.

[43] In 2022, Buckley starred as a widowed woman who travels on holiday to a countryside village in Alex Garland's folk horror film Men, alongside Rory Kinnear.

[45][46] In June 2021, Buckley joined Frances McDormand, Rooney Mara, Claire Foy and Ben Whishaw in Sarah Polley's feature adaptation of Miriam Toews' bestselling novel Women Talking, with MGM's Orion Pictures and Plan B Entertainment producing the film.

[48] In July 2022, Buckley joined Colman, Luke Evans, Jonathan Pryce and Johnny Flynn in Scrooge: A Christmas Carol, an animated rendition of the Charles Dickens' classic, which was released on Netflix in December 2022.

[50][51] That same year, it was announced that Buckley would replace Carey Mulligan as the lead in Christos Nikou's English-language feature film debut Fingernails.