McGavin progressed through Ipswich Town’s youth system after joining their academy in 2009 and signed his first professional contract on 8 February 2019. Following brief loan spells at Bury Town and Concord Rangers, he made his Ipswich debut on 12 November 2019. Ipswich extended his contract by a year on 6 May 2020, and he signed a new two-year deal with an option for an additional year on 9 September 2020. He left Ipswich at the end of the 2021–22 season when his contract expired.
On 1 February 2021, McGavin joined Ayr United on loan until the end of the 2020–21 season, making his debut on 5 February 2021. He then signed on loan for King’s Lynn Town for the 2021–22 season, debuting on 28 August 2021. Released by Ipswich in 2022, he signed a three-year contract with Torquay United. On 4 June 2024, McGavin joined newly promoted Yeovil Town on a two-year deal.
