*Club domestic league appearances and goals, correct as of 18:27, 9 November 2024 (UTC) ‡ National team caps and goals, correct as of 20:26, 1 October 2021 (UTC)
Having started his senior career at Glentoran, Conn-Clarke joined Premier League club Burnley as a scholar in 2018. He had a spell on loan at Chorley in 2020 and signed for Fleetwood Town on EFL League One in February 2021, making his debut in September of that year.
Having previously played for Linfield's youth academy, he joined Glentoran aged 11.[3] In summer 2017, he was offered a scholarship by English Premier League club Burnley, but remained at Glentoran for the 2017–18 season due to his age.[4] He made his senior debut for Glentoran on 28 April 2018 as a substitute in a 3–1 defeat to Ballinamallard United.[5] He joined English Premier League club Burnley on a two-year scholarship in summer 2018.[2][6] In summer 2020, he was given a one-year extension to his scholarship.[7] In October 2020, he joined National League North club Chorley on a work experience loan,[8] where he made 2 appearances.[5]
In February 2021, it was announced that Conn-Clarke had joined Fleetwood Town on an 18-month contract with an option to extend by a year.[9][10] On 1 July 2021, Fleetwood Town announced that his contract had been extended until the end on the 2022–23 season, with the option of a further year.[11] He made his debut for the club on 25 September 2021 as a substitute in a 2–2 draw away to Cambridge United.[12] On 4 February 2022, he was sent out on loan to National League side Altrincham on an initial one-month loan.[13] In July 2022, Conn-Clarke returned to Altrincham until January 2023.[14]
On 16 June 2023, Conn-Clarke signed for National League side Altrincham for a club record fee.[16] Having scored twenty-three goals and assisted a further twelve, he was named National League Player of the Year for the 2023–24 season.[17] Following his stellar season, Conn-Clarke was linked with moves away from Altrincham with a host of League One clubs interested.[18]
On 17 June 2024, Conn-Clarke signed for EFL League One side Peterborough United for an undisclosed fee on a three-year deal with an option for a fourth.