Chambers was a second-year scholar when he was involved with the Gillingham first-team in February 2022, becoming the fifth youngest player in the club's history to be named in a first-team squad.[1] He made his EFL League One debut on 12 March, after coming on as a 75th-minute substitute for Charlie Kelman in a 1–0 win at Doncaster Rovers.[2] He won his first start on 2 April, in a 1–0 defeat at Sunderland; manager Neil Harris said that "he's got real personality and character. That's why I played him".[3]
He appeared to have left the club after rejecting a new contract offer and trialling with Tottenham Hotspur at the end of the 2021–22 season.[4][5] However, he eventually signed a new contract in September 2022.[6]
On 6 November 2022, he joined Worthing of the National League South on a short-term loan deal.[7] He impressed manager Adam Hinshelwood, who said he would and try to extend the teenager's loan deal.[8] In January 2023, it was confirmed that Gillingham had agreed to extend his loan until the conclusion of the 2022–23 season.[9] After 26 appearances and three goals for Worthing, Gillingham recalled Chambers from his loan on 20 April 2023.[10]
On 11 November 2023 Chambers joined National League South side Welling United on loan for an initial period of one month, making his league debut for the side in a 4–3 win over Slough Town the same day.[11][12]
On 22 March 2024 Chambers re-joined Worthing on loan until the end of the 2023–24 season.[13]
On 6 August 2024, Chambers signed for Isthmian League Premier Division side Folkestone Invicta following his departure from Gillingham.[14][15] He was released by the club on 18 September 2024 after just five appearances.[16][17]
On 10 January 2025, Isthmian League Premier Division side Chatham Town announced that Chambers had signed for them.[18]