Čeliković started his professional career at Rijeka, who loaned him to Inter Zaprešić in 2018 and to Zrinjski Mostar in 2019.
Čeliković started playing football at local clubs, before joining Rijeka's youth academy in 2015.
[4] In June 2019, he was loaned to Bosnian side Zrinjski Mostar until the end of season.
[6] On 10 July 2023, Čeliković joined Russian Premier League club Akhmat Grozny on a season-long loan with an option to buy.
[7] In July 2024, Čeliković joined Super League Greece club Panetolikos on a season-long loan deal after Akhmat Grozny had activate their option to buy.