Conte joined Siaka Académie Foot at the age of eight. In 2022, he joined Flamme Olympique, where he played a few matches across six months before returning to Siaka Académie Foot.[1] In December 2022, Conte participated in two friendly matches with Ligue 2 side Bastia.[3] On 29 June 2023, he signed for the club on a one-year contract with an option for a two-year extension.[4] On 26 August 2023, Conte made his professional debut for Bastia as a 65th-minute substitute in a match against Troyes.[5] He scored two goals in the 70th and 80th minutes to lead Bastia to a 3–2 victory.[6][7] He switched to BSC Young-Boys in Summer 2024 and signed a contract until 2029.[8]