Dervişoğlu joined the Sparta Rotterdam academy at the age of 10 and broke into the club's reserve team early in the 2017–18 Tweede Divisie season.

[1][3] Dervişoğlu was a regular in the first team squad during the 2018–19 Eerste Divisie season and he helped the club to promotion back to the Eredivisie through the end-of-season playoffs.

[7] Down the pecking order for the attacking positions,[8] Dervişoğlu made 7 appearances during the remainder of the 2019–20 season,[9] which ended with defeat in the 2020 Championship play-off final.

[13][18] Despite being named in each of head coach Thomas Frank's first four matchday squads of the 2021–22 season, Dervişoğlu made just one appearance, with a start in a 3–1 EFL Cup second round win over Forest Green Rovers.

[17][20] Dervişoğlu made just one seven-minute substitute cameo during the opening month of the 2022–23 Premier League season and well down the attacking pecking order,[17] he joined Championship club Burnley on a season-long loan on the final day of the summer transfer window.

[21] Dervişoğlu played just 71 minutes across 9 substitute appearances in all competitions during his spell, with his only goal coming with an injury time winner in a 3–2 victory over Rotherham United on 2 November 2022.

[24] On 9 February 2024, after scoring four goals in 20 predominantly substitute appearances,[17] he joined Süper Lig club Hatayspor on loan until the end of the 2023–24 season.