Colley studied at the Oxford School of Drama where, as a student, she performed in productions of Anna Karenina, The Taming of the Shrew, and Pride and Prejudice.
In 2014, Colley made her stage debut in The Crucible at The Old Vic theatre in London. Colley was nominated for Best Supporting Actress in a Play at the 2015 WhatsOnStage Awards for her performance as Abigail Williams, but lost out to Rachelle Ann Go.
In 2017, Colley starred as Mileva Marić in Genius, the ten-part television series for National Geographic and Fox 21 about the life and work of Albert Einstein. In 2018, Colley reappeared in the second season of Genius, playing Dora Maar the lover of Picasso, who was played by Antonio Banderas.