[2][3][4] She studied for a degree in Acting at the Queen Margaret University School of Drama in Edinburgh, achieving a first, and was awarded the Laurence Olivier Bursary in 2000.

She took the starring role of the jazz singer Jessie in the BBC Two Stephen Poliakoff six-part 2013 drama serial Dancing on the Edge, alongside Chiwetel Ejiofor, John Goodman, Matthew Goode, Anthony Head, and Jacqueline Bisset.

[8] Coulby returned to the stage for the first time since 2014 in Rupert Goold's Albion at the Almeida Theatre in February 2020, which was filmed and broadcast on BBC Four in August 2020.

[9] Coulby joined the cast of the Apple TV+ thriller Suspicion, which is a remake of the Hebrew-language series False Flag in March 2020.

[10] Coulby plays Vanessa Okoye, the investigator questioning the "five Brits, quickly pinpointed as the potential suspects" of the kidnapping in the thriller.