Souttar played for the Dundee United development team, including alongside his brother John in February 2015. Having featured in a number of match day squads and having been listed as a substitute for the first team, Souttar signed a contract extension in December 2015, tying him to Dundee United until May 2018. He made his first team debut against Partick Thistle in a Scottish Premiership match on 10 May 2016 and scored his first senior goal against Kilmarnock four days later.
English Premier League club Stoke City became interested in signing Souttar, and although Dundee United rejected two bids to buy the player during June 2016, it was reported during August 2016 that the clubs had agreed an initial £200,000 fee for his transfer
He officially joined Stoke on 29 September 2016, signing a three-year contract for an undisclosed fee. Souttar made his Stoke debut on 23 August 2017 in a 4–0 EFL Cup win over Rochdale.
After signing a new contract with Stoke, Souttar joined Scottish Premiership side Ross County on 24 January 2018 until the end of the season.