[6] After impressing manager Magnus Haglund, Kurtulus ended the season making 11 league appearances, of which he started ten, mostly as a right-back.
[11] On 20 February 2022, he made his debut with Hammarby in the 2021–22 Svenska Cupen group stage against Falkenbergs FF after coming on as a substitute at 62nd minute in place of Simon Sandberg.
[14] Kurtulus featured in the final of the 2021–22 Svenska Cupen, in which Hammarby lost by 4–5 on penalties to Malmö FF after the game ended in a 0–0 draw.
[17] In August the same year, the club reportedly accepted an offer worth around €3 million from Sturm Graz for his transfer, but Kurtulus turned down the move.
[21] On 29 August 2020, Kurtulus received a call-up from Kosovo U21 for the 2021 UEFA European Under-21 Championship qualification match against England U21,[22] and made his debut in the 0–6 loss after being named in the starting line-up.
[28] His debut with Sweden came on 9 June in the 2022–23 UEFA Nations League match against Serbia after coming on as a substitute in the 42nd minute in place of Joakim Nilsson.