Cleworth started his career with Wrexham.[2] He signed his first professional contract at Wrexham in 2020.[3] In 2021, he signed for Welsh team Caernarfon Town on a six-month loan.[4] In December 2022 he signed a new deal for Wrexham until 2025.[5]
Cleworth's first league goal was a late winner in a 2–1 win against Colchester United on April 6, 2024.[6]
On August 10, 2024, Cleworth scored the first League One goal for Wrexham in 19 years as Wrexham won in their first game after promotion. It was also his 100th career appearance for the club across all competitions.[7]