*Club domestic league appearances and goals, correct as of 15:39, 7 January 2025 (UTC) ‡ National team caps and goals, correct as of 13:31, 9 Dec 2024 (UTC)
Cleary progressed through West Bromwich Albion's academy, and began training with the club's first team in the 2021–22 season after impressive form for the club's under-18 and under-23 teams.[1][2] He was offered a professional contract by the club in December 2021.[3] He was nominated for the Premier League 2 player of the month award for December 2021.[4] He made his senior debut as a substitute in a 2–1 FA Cup defeat to Brighton & Hove Albion on 8 January 2022.[5]
On 20 August 2024, Cleary joined League Two club Walsall on a season-long loan deal.[6] He was recalled on 7 January 2025.[7]