McGee turned professional at Spurs in July 2014, and in October 2015 signed a new contract to keep him there until 2019. He was loaned to Peterborough United on a four-month deal. He made his debut in the EFL on 10 September, in a 2–2 draw with Port Vale. In July 2017, he joined Portsmouth, with a 3 year contract, and was later loaned to Bradford city, in the middle of the 2019-2020 season.
McGee moved to Forest Green Rovers on 15 July 2020 on a two-year deal and was awarded the EFL League Two Player of the Month award for January 2022 after conceding just one goal in six matches. In January 2023 he was loaned to Derby County until the end of the 2022-2023 season.