Gleaves's first theatre part was as an extra in Don Carlos at the Royal Exchange Theatre in Manchester. He did several plays there including the lead in Macbeth. His theatre credits include The Front Page at the Donmar in 1997, Alan Jeffcote in Hindle Wakes by Stanley Houghton at the Royal Exchange, On the Shore of the Wide World in 2005 first at the Royal Exchange Theatre and then at the Royal National Theatre, Dr Faustus in 2010, Chair in 2012 at the Lyric Theatre Studio, Hammersmith, and The Saga of Noggin the Nog in spring 2013.
He has been in many television shows since 1992; Gleaves was Rick Powell in the television drama series Playing the Field. He had the role of Ray Fairburn in Conviction. Conviction was filmed at Salford Lads' Club which delighted Gleaves because of the building's connection to The Smiths. In The Chase, he was the father Tom Bedford. In 2009, he said the idea for Survivors, in which he played the scientist Whitaker, was "great". He played DS Andy Roper in the first two series of Scott & Bailey. In 2019, Gleaves played the title role in the 2019 revival of the classic CBBC series The Demon Headmaster.
More recent screen credits include The Rising, The Crown, Silent Witness, After the Flood, The Bombing of Pan Am 103, and Riot Women.
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