On the beginning of the 2015–16 season he became the second youngest captain in history of the club, Giuseppe Gjergja being the only younger one in 1957.

[4] In November, 2021, Bašić signed with Jazine, the development team of Zadar competing in the Croatian second-tier Prva muška liga.

On February 9, 2022, Bašić signed with HKK Posušje of the Basketball Championship of Bosnia and Herzegovina.

[9] On 20 July 2023, Bašić signed with Nevėžis Kėdainiai of the Lithuanian Basketball League (LKL).

With the Croatia national under-16 team, he played at the 2011 FIBA Europe Under-16 Championship where he won gold.