He is known to television audiences for his roles as Detective Constable Gary Boyle on the sitcom The Thin Blue Line (1995–96), Bill Miller on the American sitcom Still Standing (2002–06), Andy Richmond on Trollied (2011–13), Hercules on Atlantis (2013–15), and King Robert Baratheon on the first season of Game of Thrones (2011).

[6] In 2011, He portrayed King Robert Baratheon in the HBO series Game of Thrones: Addy's audition for the role was, according to showrunners David Benioff and D. B. Weiss, the best they saw, he being the easiest actor to cast for the show.

[8] He portrayed Hercules, one of the main characters in the BBC One fantasy drama series Atlantis,[9] which started airing on 28 September 2013 in the UK.

In the BBC television drama New Blood (2016),[4] featuring young detectives from the Serious Fraud Office and the London Police Service, Addy played D.S.

Addy portrayed David Philby in The Time Machine[4] and made an appearance as the Ship Captain in Around the World in 80 Days[5] with Jackie Chan and Steve Coogan, and made an appearance as Friar Tuck in Ridley Scott's 2010 film Robin Hood.

[20] On 20 July 2019, Addy was awarded an honorary doctorate from the University of York, having given a speech at the Roses Varsity opening ceremony a few months prior.