She played Cassie in Skins (2007–2008, 2013) and Gilly in the HBO fantasy series Game of Thrones (2012–2019), for which she has been nominated along with her castmates for three Screen Actors Guild Awards.

She impressed the producers of the series and was cast as Cassie Ainsworth, a gentle and creative but self-destructive teenager with an eating disorder.

[8] Following Skins in May 2008, Murray made her stage debut as Mia in the critically acclaimed That Face, a West End production at the Duke of York's Theatre.

In early January, she appeared in the British television thriller Above Suspicion: the Red Dahlia,[11] an adaptation of Linda La Plante's novel, in a small role.

In 2013, Murray appeared in a two-episode feature, in the seventh and final series of Skins, where she reprised her role as a more serious, solemn, and independent adult Cassie Ainsworth.

[15] Murray starred in Lily & Kat (2015), an independent American film and the first feature directed by Micael Preysler, about inseparable best friends who struggle to make the best of their last few days together, savouring the city nightlife with an enigmatic artist one of them takes a liking to.

In 2016 Murray played Sylvia Ageloff, a young Jewish American intellectual from Brooklyn and a confidante of Trotsky, in the film The Chosen.

[16] In 2018, she played the lead role of Leslie "Lulu" Van Houten, the American convicted murderer and former member of the Manson Family, in the film Charlie Says by Mary Harron.

The movie premiered at the 75th Venice International Film Festival and was based on the books The Family, by Ed Sanders, and The Long Prison Journey of Leslie Van Houten, by Karlene Faith.