Compston was born the second of 2 boys, with an elder brother, and brought up in Greenock, Inverclyde, and attended St Columba's High School in neighbouring Gourock.
A promising footballer, he was on the books of Aberdeen as a young teenager, and after leaving school he signed for the local professional team Greenock Morton. Compston made two first team appearances in the 2001–02 season, in which the team were relegated to the Third Division. In both matches he appeared as a substitute and Morton lost 4–0, to Alloa Athletic and Queen of the South.
Having never acted before, Compston successfully auditioned for the lead role in Ken Loach's Sweet Sixteen, which was being filmed locally. The film's success at the Cannes Film Festival gave him instant celebrity status in Scotland. Both he and his co-star William Ruane were nominated for Most Promising Newcomer at the British Independent Film Awards, with Compston winning the category.
His subsequent film career was comparatively low-key, as he wanted to "serve his apprenticeship" with a regular role in the BBC TV drama serial Monarch of the Glen. He then appeared in three films: A Guide to Recognizing Your Saints (Jury Prize and Best Ensemble Cast at the Sundance Festival) with Robert Downey, Jr.; Red Road (Jury Prize at Cannes), shot in Scotland with Kate Dickie and Tony Curran, for which he was nominated as Best Supporting Actor at the Scottish BAFTAs; and True North with Peter Mullan and Gary Lewis, for which he was nominated as Best Actor at the British Independent Film Awards.
Compston starred in the 2010 film Soulboy, alongside Craig Parkinson, playing the role of Joe McCain. He also appeared in the horror film The 4th Reich as Private Newman, and made a cameo appearance in a low-budget web series, "Night is Day".
Compston appeared in The View's music video for "Grace" and "How Long," as he is friends with the band.
In 2012 Compston starred in the lead role of Detective Sergeant Steve Arnott, a detective on an anti-corruption squad, in the BBC police drama Line of Duty, acting alongside Craig Parkinson once more.
In 2012 Compston also starred in the violent thriller Piggy. Going back to his Scottish roots, he then appeared in the lead role in The Wee Man, directed by Ray Burdis, a film depicting the life of the Glasgow gangster Paul Ferris. It was released in the UK in January 2013.
In April 2013 Compston starred in the ITV mini-series The Ice Cream Girls.
Compston appeared as Roy James in The Great Train Robbery.
In 2014, 2016 and 2017 Compston reprised his lead role of Detective Sergeant Steve Arnott in the second, third and fourth series of BBC Two police drama Line of Duty, which moved to BBC One at the start of the fourth series.
In 2016 he starred in the three-part Scottish television drama series In Plain Sight as a serial murderer, Peter Manuel, who is pursued to his conviction and ultimate execution by the detective William Muncie.
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