Biuk made his debut for Hajduk on 2 March 2021, in a Croatian Cup 3–0 victory over Zagreb, being substituted on for Jairo in the 74th minute.[6][4] He made his Prva HNL debut on the 20 March 2021, starting on the left wing in Hajduk's 1–0 derby win against Šibenik, due to absence of Alexander Kačaniklić, Dimitris Diamantakos and Umut Nayir. After the match, coach Paolo Tramezzani gave Biuk no significant amount of playtime until the 2–0 derby defeat to Dinamo Zagreb on 25 April.[2] Since then, Biuk became a regular for Hajduk, scoring three goals and delivering two assists by the end of the season.[7][8] He scored his debut goal for Hajduk on 1 May, in a 3–2 derby victory over Rijeka.[9] On 22 May, he scored in a crucial 2–0 victory over Lokomotiva Zagreb, securing a Europa Conference League qualifying spot for Hajduk.[10]
On 25 January 2024, Biuk was loaned to Segunda División side Real Valladolid, until the end of the season.[13] On 8 July, after the club's promotion to La Liga, his buyout clause was activated,[14] and he signed a permanent five-year deal with the Pucelanos.[15]
Loan to Hajduk Split
Biuk made his return to Hajduk Split on a one-year loan move on 1 September 2024 from Valladolid. He will be wearing the number 27 shirt again, just as he did when he played for Hajduk Split two years ago.[16]
Stipe Biuk was born in Split and grew up in Solin. His father Robert Biuk is a retired policeman who hails from Vrlika.[2][4][18] His mother Danijela Boduljak passed away on 28 December 2011 while making a birthday cake for Stipe, collapsing in the kitchen due to a ruptured aneurysm in her head.[19][20] His brothers Filip and Duje are also football players, playing for Mosor and Krško 1922 respectively.[2]