Born and raised in Enfield in North London, Stewart joined Tottenham Hotspur's Academy in 2010 at the age of 17. In four years at Spurs he failed to make a senior appearance but was loaned out just once, to Crewe Alexandra towards the end of 2012/13. When his contract expired in 2014 Liverpool snapped the defensive midfielder up on a free transfer. In January 2015 he joined Cheltenham Town on loan but was recalled after a month due to injury. During his spell there he scored once in four appearances. On transfer deadline day he was loaned to League Two side Burton Albion where he played seven games, scoring twice and helping the Staffordshire side to promotion.

Stewart was loaned to Swindon Town at the start of 2015/16 where he was unfortunate to suffer knee ligament damage which restricted his number of appearances before Christmas to just eight. As injuries mounted at Anfield he was recalled in January 2016 and made his debut at Exeter City in the 3rd round of the FA Cup. He started all four of Liverpool's FA Cup games and although never spectacular, he did the basics well. He was rewarded with a four-year contract and started six times in the league towards the end of the season as Jurgen Klopp rotated his squad with the Europa League campaign in mind. Stewart's starts in 2016-17 were limited to four in cup competitions. He came off the bench four times in the league but the last of these was in September. He left for Hull City in the summer in a deal reported as £6 million which represented good business on Liverpool's part.

In his first season at Hull, Stewart struggled for game time, starting only ten times in the league. 2018/19 was more fruitful as he featured 27 times. He made the same number of league appearances in 2019/20 when Hull were relegated to League One. He was released and failed to find a new club in the next transfer window, but on 23rd January 2021 agreed an 18 month deal with League One side Blackpool. He helped them to promotion via the play offs, but was unfortunate to be ruled out of the start of the new campaign due to injury. He had a frustrating 2021/22 season making just twelve appearances. However he did make his international debut for Jamaica, playing in World Cup qualifiers against Panama and Costa Rica in early 2022. The following season was a frustrating one in which Stewart failed to make an appearance after a succession of injury problems. After he was released he relocated to Dubai, setting up as a performance coach.