[16] Abbott made his feature film debut in the 2011 drama thriller Martha Marcy May Marlene opposite Elizabeth Olsen.

[18] The same year, Abbott made his Broadway debut in the revival of the play The House of Blue Leaves opposite Ben Stiller and Edie Falco.

[23] Abbott gained public recognition for his role as the docile boyfriend of Marnie (Allison Williams), Charlie Dattolo in the HBO comedy-drama series Girls.

Abbott quit the series after the show’s season-two finale, stating that the reason why he left was because he couldn't relate to the character.

[27] After leaving the series, Abbott returned to the theatre in the fall of 2013 in the play Where We're Born by Lucy Thurber at the Rattlestick Playwrights Theater.

Starring Oscar Isaac and Jessica Chastain, the film had its world premiere at the AFI Fest on November 6, 2014, at the Dolby Theatre in Hollywood and received a limited release on December 31, 2014.

[36] Abbott starred as the title character in the drama James White opposite Cynthia Nixon, directed by Josh Mond.

[40] In 2016, Abbott co-starred in the comedy war film Whiskey Tango Foxtrot, opposite Tina Fey and Martin Freeman, released on March 4, 2016.

[45] Abbott starred alongside Joel Edgerton and Riley Keough in Trey Edward Shults's horror film It Comes at Night, which was released on June 9, 2017.

[46] He co-starred in Jamie M. Dagg's 2017 thriller Sweet Virginia, opposite Jon Bernthal, Imogen Poots and Rosemarie DeWitt.

[50] In 2021, Abbott starred in John Michael McDonagh's The Forgiven,[51] followed by Zachary Wigon's second feature film Sanctuary in 2022[52] and Yorgos Lanthimos' Poor Things in 2023.

[53] In 2023, he also returned to TV in the role of Stan in the Apple TV+ anthology series The Crowded Room, alongside Tom Holland and Amanda Seyfried.

[56] In February 2022, it was announced that Abbott would reteam with John Michael McDonagh in Fear Is The Rider, co-starring Abbey Lee.

[57] In May 2022, he signed to star in Justin Anderson's directorial debut Swimming Home, an adaptation of the Booker Prize-nominated novel of the same name by Deborah Levy.

[58] He has also voiced Reed, an art dealer, in the adult animated music television series Entergalactic, based on the album of the same name by American musician and actor Kid Cudi.

[60][61][62] In September 2023, it was reported that Abbott would join Florence Pugh in the Netflix adaptation of John Steinbeck's novel East of Eden, in the role of Adam Trask.