After playing for Garforth Villa at youth level,[4] and coming through Leeds United's academy, Jenkins signed a two-year scholarship with the club in April 2018.[5] Jenkins signed his first professional contract on 15 January 2019, with the contract lasting until the summer of 2021.[6] He signed a new contract in November 2019, lasting until summer 2023.[2] He played for Leeds United U21's against Barrow in the EFL Trophy on 5 October 2020.[7] He was first named on the Leeds bench on 7 November 2020 for a fixture against Crystal Palace.[8][9] Jenkins made his senior Leeds debut on 10 January 2021 in the 3–0 FA Cup third round defeat against Crawley Town as a half-time substitute.[10] On 8 September 2023, Jenkins joined Scunthorpe United on loan until January 2024.[11]