Compton was released by Nottinghamshire at the end of the 2021 season.[6] In the off-season he joined Kent on a two-year contract.[7] During the 2021/22 English off-season he played for Mountaineers in Zimbabwean cricket.[8] On 17 November 2021, in the 2021–22 Pro50 Championship match against the Rhinos, Compton scored his first century in List A cricket with 102 runs.[9] In February 2022, in the 2021–22 Logan Cup, Compton also scored his maiden century in first-class cricket.[10] Compton finished as the leading run-scorer in the 2021–22 Pro50 Championship, with 361 runs in eight matches,[11] and was named the Batter of the Tournament.[12]
Compton made his Kent debut in the first match of the 2022 season, where he scored a century, the third of his first-class career.[13][14] A week later, in Kent's second match of the season, Compton scored his second and third centuries for the team,[15]carrying his bat in the first innings and being the last batter dismissed in the second.[16] He continued to score heavily and came close to achieving 1,000 first-class runs before the end of May, something only achieved nine times previously, the last in 1998. He had made 878 first-class runs in the County Championship in April and May before scoring 158 runs (in two innings combined) in the last match before the end of May, a red-ball two-innings match for a "First Class Counties XI" against the touring New Zealanders in a match that was not given first-class status as the sides used more than eleven players at different stages.[17][18] He reached the 1,000 run milestone in June, having scored four centuries and five half-centuries during the season to that point.[19]
At the end of the season, Compton was voted Kent's Men's Player of the Year.[20][21] During the 2022—23 English winter, he returned to Zimbabwe, playing again for Mountaineers. He passed his previous highest first-class score of 140 in a match against Eagles in December, making 154 runs, before scoring his maiden double-century later in the month. His score of 217 came against Southern Rocks in an opening partnership of 228 runs with Joylord Gumbie.[22][23] He signed a new Kent contract later the same month, keeping at the club until the end of 2024.[21] In Kent's opening match of the 2023 season, Compton scored another century, matching his performance in scoring a century in the opening match of the previous season with an unbeaten 114 runs.[24]
