The following season, Barišić played in 28 games, managing one goal and two assists from left back as Osijek narrowly avoided relegation.

Despite his club's struggles, Barišić's performance for Osijek in the 2014–15 season saw him earn a move to league champions Dinamo, signing a five-year contract.

Osijek were purchased in February 2016 by Hungarian oligarch Lőrinc Mészáros and Croatian entrepreneur Ivan Meštrović, the first time the club had gone into private ownership.

The new ownership identified Barišić as the type of player they want representing the club; young, talented and produced by the youth academy.

[10][11] On 22 August, Dinamo Zagreb executive Zdravko Mamić was shot in his native village of Zidine, Bosnia and Herzegovina.

[12] The shooting was believed to be an assassination attempt organized by the Čepin Mafia clan, of which Barišić's father Stipe is a member.

[18] On 18 February 2021, in his hundredth appearance for the club, Barišić scored a brace from the penalty spot in a 4–3 away win over Royal Antwerp in the Europa League Round of 32.

[19] On 25 June 2024, Turkish side Trabzonspor announced that Barišić would join the club on a free transfer, signing a three-year deal.