Clarke was born in London, England. He has had recurring television roles as Wyman Norris in the revived series of Auf Wiedersehen, Pet (2002–2004) and as Mickey Smith in the first two series of the revival of the BBC science fiction series Doctor Who (2005–2006). He notably became the series' first black companion in the episode "School Reunion", and reprised his role as Mickey in the episode "Journey's End" in 2008 and in 2010 in "The End of Time" Part 2, and also starred in the Doctor Who audio series Dalek Empire: The Fearless, which was released from September to December 2007. His other television work includes appearances in Casualty and Metrosexuality. He has also acted on the stage, and won the Laurence Olivier Award for "Most Promising Newcomer" in 2003 for his performance in the play Where Do We Live at the Royal Court Theatre. Clarke starred in the film Doghouse, directed by Jake West and produced by Carnaby Films International. The film was shot primarily in Midhurst, a small town in West Sussex, on the grounds of the old King Edward VII Hospital. He also participated in Neil Marshall's film Centurion, about which Clarke said, "it's about the Roman Legion and I'm one of the soldiers".
Clarke began his writing career in 2005 when he wrote the screenplay for the film Kidulthood which was released in 2006. He also directed and starred in the sequel, Adulthood, which was released in 2008. On directing his first film, Clarke described his experience, "Directing for the first time was definitely a challenge and tiring at times. It was a steep learning curve and if you're willing to do stuff and go with it, then it pays off." His other writing credits include "Combat" which is an episode of the Doctor Who spin-off series Torchwood, and West 10 LDN, a pilot for BBC Three which is about kids on a rough housing estate.
In 2009, Clarke was awarded a BAFTA award in the category of Orange Rising Star Award. As a result of the success of Kidulthood, Adulthood, and his BAFTA win, he was ranked at number 83 in the MediaGuardian 100, an annual ranking of media people in The Guardian.
He also played the role of A.J.,opposite Jim Sturgess, in Philip Ridley's cult film, Heartless. Clarke has worked with BBC Blast, a project for teenagers that aims to inspire and get people being creative. Shortly after his BAFTA win he gave a talk to inspire young people telling them to "broaden your mind". His next project, 18.104.22.168, a heist movie, was released on 2 June 2010 starring Tamsin Egerton, Emma Roberts and Adam Deacon. The film was shot in London and New York. He has also played an uncredited role in 2012's Ghost Rider: Spirit of Vengeance as a priest. The scene was cut from the movie, but can be seen in the Deleted Scenes in the Special Features of the DVD. He played Thomas Harewood in Star Trek Into Darkness, a family man with a wife and young daughter. The film was released on 15 May 2013.