Cooper joined the Swansea youth academy at under-12 level and signed his first professional contract with the club in February 2019. Cooper made his professional debut with Swansea in a 2–0 FA Cup win over Stevenage on 9 January 2021. He scored his first goal for Swansea on 23 January 2021 in a 5–1 win over Nottingham Forest in the FA Cup fourth round.
On 31 August 2021, Cooper joined League Two side Newport County on a season-long loan deal, with the option of him returning to his parent club in January 2022. He made his debut for Newport the same day in the starting line-up for the 2–0 win against Plymouth Argyle in the EFL Trophy. Cooper scored his first goal for Newport on 2 October 2021 in the 3–0 League Two win against Scunthorpe United.
On 1 September 2025 Cooper joined EFL League One club Wigan Athletic on loan for the remainder of the 2025–26 season. On 2 January 2026, he returned to his parent club.