He is widely known for his roles as Tom Branson in the ITV period drama Downton Abbey (2010–2015) and Paul Prenter in the biopic Bohemian Rhapsody (2018).

[1] Leech became interested in acting at 11 when he was given the part of the Cowardly Lion in a school production of The Wizard of Oz and found he loved being on stage.

[2] He recalled how he immediately decided to become an actor when Peter McDonald told him how acting is a profession on the last night of the production's run.

[7] He landed his first major roles in Cowboys & Angels and Man About Dog while at Trinity, and he has admitted that he did little schoolwork because he spent his time on auditions and acting.

[11][12] Leech played the role of Shane Kirwan in the Ireland's RTÉ series Love Is the Drug, in which he received a Best Actor nomination from the Irish Film and Television Awards.

In 2007, Leech appeared in the HBO drama series Rome as Marcus Agrippa, Octavian's top soldier and friend.

Leech also appeared in ITV 2010s television series Downton Abbey as chauffeur Tom Branson, whose twin beliefs in socialism and Irish Republicanism clash with those of the British upper class.

[18] Leech played Paul Prenter, who was briefly Freddie Mercury's manager and lover, in the biopic Bohemian Rhapsody (2018),[19] which earned him a nomination for Outstanding Performance by a Cast in a Motion Picture at the 25th Screen Actors Guild Awards.