Barišić started his professional career at Osijek, playing first in its reserve team, before being loaned to Frosinone in 2022. The following year, he moved to Basel.
A former youth international for Bosnia and Herzegovina, Barišić made his senior international debut in 2023.
In January 2022, he was loaned to Italian side Frosinone until the end of the season.[3] On 12 March, he scored his first professional goal in a triumph over Alessandria.[4]
Basel
In August 2023, Barišić was transferred to Swiss outfit Basel for an undisclosed fee.[5] He made his official debut for the team against Zürich on 3 September and scored an own goal.[6] On 6 October 2024, he scored his first goal for Basel against Young Boys, which secured the victory for his squad.[7]