Reece joined Brentford as a scholar/trainee in 2014 and turned professional in April 2016 but only made a solitary substitute appearance in the league for the Bees. Loan spells followed with Newport County, Yeovil Town, Maidenhead United, Macclesfield Town and Partick Thistle before he had a short period with Queens Park Rangers under-23 squad ahead of signing for  Dunfermline Athletic in 2021. 

After making ten league league appearances for the Fife club, he was released in May 2022 and spent the 2022/23 season playing non-league football firstly with Cherstsey Town and then Hayes & Yeading United. 

After appearing against Tiverton Town in a pre-season friendly, the 25-year-old Reece agreed a deal with Exeter City in July 2023. Coming on as a substitute, he was one of eight players to make his Grecians’ debut in the win at Wycombe Wanderers on the opening day of the 2023/24 season. He subsequently scored his first goal for the club, a stoppage time winner, against Reading in the fifth league game of the season. With another six strikes in the league - against Carlisle, Barnsley, Peterborough, Burton, Cheltenham and Stevenage - Reece finished the season as City's top scorer as he started 30 league games with another nine appearances from the bench.