[6] His best junior result was winning the boys' singles title at the 2023 French Open, where he defeated Juan Carlos Prado Ángelo in the final.

[7][8] In April 2022, Prižmić reached his first ITF final at a clay-court tournament in Dubrovnik, Croatia, where he lost to Gergely Madarász in straight sets.

Prižmić made his ATP debut in the singles draw of the 2022 Croatia Open Umag as a wildcard where he lost to Bernabé Zapata Miralles in the first round by retirement.

[9] In April, Prižmić then qualified for the Banja Luka Open in Bosnia and Herzegovina, but fell to Richard Gasquet in the first round.

[10] He then defeated Zsombor Piros to reach his maiden ATP quarterfinal, losing to eventual champion Alexei Popyrin.

At the Australian Open, Prižmić defeated Mariano Navone, Duje Ajduković and Aziz Dougaz to qualify for his first Grand Slam.