[2] McGeever began his career with Queen's Park, and signed for Falkirk in the summer of 2012[3] also spending time with Brechin City and Dumbarton, where he was club captain.
McGeever joined Falkirk in the summer of 2012, making his first team début in the Scottish Football League First Division against Dumbarton on 20 October 2012.
[11][12] After impressing in his performances for Queen's Park during the 2016–17 season, McGeever subsequently signed for recently promoted Scottish Championship club Brechin City on 12 June 2017.
[15] After another impressive season at the Rock, he turned down offers from elsewhere to sign a new two-year deal with the Sons in May 2021 – despite the club not having a manager in place at the time.
[20] After struggling for game-time as he recovered from a long-term injury, McGeever moved to Scottish League One side Clyde on loan in February 2023 - with Peter Grant going in the opposite direction.