Varma was raised in Bath, Somerset, the only child of an Indian father and a Swiss mother who was of part Genoese Italian descent.

[11] Varma guest starred in the fourth-season premiere of hit US detective drama Bones as Scotland Yard Inspector Cate Pritchard.

Later on, she also gave her voice to Katherine Proudmoore in Battle for Azeroth, one of the most recent expansion in the MMO role-playing game World of Warcraft.

In 2016, she played the lead role of DC Nina Suresh in the eight-episode British television drama Paranoid, streamed worldwide on Netflix.

Varma portrays a reform-minded corrections official in the 2020 ABC legal drama For Life, and appears as the double agent Tala Durith in the Obi-Wan Kenobi series for Disney+, as well as Mission: Impossible – Dead Reckoning Part One.

[19] In 2014, Varma played Tamora, Queen of the Goths, in Lucy Bailey's "gore-fest" production of Titus Andronicus at Shakespeare's Globe.

[21] In 2020, pre-lockdown, she starred in Chekhov's The Seagull as Irina alongside Game of Thrones co-star Emilia Clarke at the Playhouse Theatre.

Her 2019 performance in Present Laughter at The Old Vic theatre earned Varma a Laurence Olivier Award for Best Actress in a Supporting Role.