Defender Cleworth began his footballing career playing youth football for the likes of Frodsham and Connah's Quay before being recommended to Wrexham at the age of 12.
Cleworth began with the under-13 group and spent his formative years at the Racecourse Ground. He was first involved in the first-team set-up aged 17 when making his debut in the Scottish Challenge Cup against Ayr United, going on to also face St Mirren Colts and Rangers Colts in the competition.
Later on in the 2019/20 campaign, he was named on the bench in the National League against Harrogate Town and Dagenham & Redbridge before the season was curtailed.
In August 2020 Cleworth was offered a first professional deal penning a contract until the summer of 2021. In January 2021 he joined Cymru Premier side Caernarfon Town on loan until the end of the season.
He made his Cofi's debut in a 2-2 draw Aberystwyth Town in the Cymru Premier coming on as a substitute in the first half, whilst he started his first game against Flint Town United playing the full 90 minutes. Cleworth's first professional goal came in a 3-0 win over Bala Town, netting a brace at the Oval. Max was part of a Caernarfon side that qualified for the European Conference play-off final, but lost out to Newtown.