[9][10] He starred in the 2017 four-part series Howards End as Leonard Bast, a young bank clerk, opposite Hayley Atwell.

[11] That same year, he starred in the short film KIN, and appeared in a season 7 episode of the HBO series Game of Thrones as Koner, a Stark soldier.

The following year, he starred alongside Molly Windsor in the thriller film Make Up and portrayed Tsarevich Pavel in the Sky Atlantic miniseries Catherine the Great.

[13] In 2020, he appeared in the BBC One series Strike and the Mangrove installment of Steve McQueen's television anthology Small Axe.

He starred with Lupita Nyong'o in the horror film A Quiet Place: Day One, directed by Michael Sarnoski, which was released in June 2024.

[24][25] In February 2024, it was announced that Quinn was cast as Johnny Storm / Human Torch in the Marvel Cinematic Universe film The Fantastic Four: First Steps (2025).