*Club domestic league appearances and goals, correct as of 13:53, 3 November 2024 (UTC) ‡ National team caps and goals, correct as of 16:30, 31 January 2020 (UTC)
Kemp joined the academy of Chelsea at the age of six, and spent ten years with the club before his move across London to West Ham United in 2015.[3]
West Ham United
Having progressed through to West Ham's U23 development squad, in which he featured in several EFL Trophy ties, Kemp moved on loan to League Two club Stevenage in January 2020,[4] followed by League One club Blackpool on a season-long loan deal in September 2020.[5] He scored his first goal for Blackpool in an EFL Trophy tie against Leeds United U21s on 11 November 2020.[6]
Leyton Orient
Kemp was recalled from his loan by West Ham on 15 January 2021,[7] and moved to Leyton Orient on a permanent basis on a two-and-a-half-year contract.[8][9]
Milton Keynes Dons
On 31 January 2022, Kemp joined League One club Milton Keynes Dons on a permanent deal for an undisclosed fee.[10][11] He made his debut on 5 February 2022 as an 88th-minute substitute in a 2–1 home win over Lincoln City.[12]
On 31 January 2023, Kemp returned to League Two when he joined Hartlepool United on loan until the end of the season.[13][14] Kemp said he saw the loan move as a 'massive opportunity' for him.[15] After scoring five times in six games, Kemp won the EFL League Two Player of the Month award for February 2023.[16] On 7 April 2023, Kemp scored his first career hat-trick in a 4–1 win against Grimsby Town.[17]
On 18 July 2023, Kemp joined League Two club Swindon Town on loan for the duration of the 2023–24 season.[18][19] Over 25 league games during the first half of the season, Kemp scored 14 goals and provided 8 assists - the second most goal contributions of any player in League Two. On 1 January 2024, he was recalled by MK Dons.[20] Despite being recalled in January, Kemp would still win Swindon's Player of the Season award.[21]
At the end of the 2023–24 season, Kemp was released by MK Dons.[22]
Stevenage
On 10 June 2024, Kemp agreed to return to League One club Stevenage on a permanent two-year contract.[23][24]