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In 2007, Jessop starred opposite Nicholas Hoult in the feature-length BBC drama Coming Down the Mountain. The writer Mark Haddon said Jessop was the inspiration behind the project. Jessop's performance was widely praised, and the film was nominated for a Television BAFTA for "Best Single Drama", before winning the RADAR People of the Year Human Rights Media AWARD 2008. Jessop made his television debut in Holby City, and has also appeared in Casualty, Monroe and Doctors. His dream is to appear on EastEnders.
In 2019, Jessop plays Terry Boyle in series 5 of Line of Duty.
Jessop is a founding member of award-winning integrated company Blue Apple Theatre, and has appeared in all their productions to date. In 2010, he played Bottom in A Midsummer Night's Dream. In 2011, he was the Mayor in Gogol's The Government Inspector. In May 2012, Jessop made history when he became the first professional actor with Down Syndrome to play the title role of Hamlet in Blue Apple's touring production. He also played the role of Terry Boyle in series one of BBC drama Line of Duty. In March and April 2013, Tommy played the role of Bobby, a victim of hate crime in Living Without Fear, Blue Apple Theatre's touring production about disability hate crime.
Jessop frequently collaborates with his brother, the writer and filmmaker William Jessop. In 2007, the brothers made the broadcast documentary Tommy's Story for Community Channel (UK). William filmed Tommy behind the scenes of Coming Down the Mountain and Holby City, and was shortlisted for Best Newcomer at the Grierson Awards 2008. In February 2014, Jessop was one of the stars of Growing Up Down's, a documentary about Blue Apple Theatre's touring production of Hamlet that William produced and directed for BBC Three. The film was described as "BBC Three at its very best"  and in November 2014 won the Creative Diversity Network Award for Most Groundbreaking Programme.
Jessop has starred in various radio productions for the BBC, including an episode of the series Stone with Hugo Speer in 2010, and the one-off play The Climb opposite Warwick Davis in 2011. On 10 April 2013, Tommy appeared in an episode of The Archers, playing Callum Longfield.
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- Episode, cast list for the week (retrieved on 2013-04-11)