In 2024 Jessop played Tommy opposite Callum Turner and Austin Butler in the TV series Masters of the Air produced by Steven Spielberg and Tom Hanks for Apple TV+.

[3][4] Jessop's performance was widely praised,[5][6] and the film was nominated for a Television BAFTA for "Best Single Drama",[7] before winning the RADAR People of the Year Human Rights Media Award 2008.

In May 2012, Jessop made history when he became the first professional actor with Down syndrome to play the title role of Hamlet[16] in Blue Apple's touring production.

[17] Jessop has also performed the roles of Prospero in The Tempest and Don Pedro in Much Ado About Nothing, Marley's Ghost in A Christmas Carol, and The Creature in Frankenstein.

[19] 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 Will produced and directed for BBC Three.

[22] The film features appearances from Kit Harington, Will Sharpe and Neve Campbell and was broadcast on BBC One on 21 August 2023 to popular and critical acclaim, including a five star review from Carol Midgley in The Times.

[23] In 2022, Jessop investigated why people with a learning disability are more than twice as likely to die from avoidable causes than the rest of the population as part of a BBC Panorama entitled Will the NHS Care for Me?

[25] 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.