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) whilst being named as North Devon Grecians' player of the year.

Such form led to Reece's contract being extended to the end of the 2025/26 campaign.