Repušic was born in the small town of Imotski, in southern Croatia's Dalmatia region, in 1978. He studied music from a young age, attending the Blagoje Bersa Music School in the city of Zadar. Repušic went on to the Academy of Music at the University of Zagreb, working with Igor Gjadrov and Vjekoslav Sutej. He took further conducting lessons with Jorma Panula and Gianluigi Gelmetti, and did apprenticeships as an assistant to Kazushi Ono at the Badisches Staatstheater Karlsruhe, and to Donald Runnicles at the Deutsche Oper Berlin. Even before turning 20, he landed a position as conductor of the Oratory Choir of the Church of St. Marka Cantores Sancti Marci in Zagreb. In 2002, he began to land guest conducting positions, and from 2006 to 2008, he was the music director of the Opera of the Croatian National Theater in Split, leading performances of core Italian opera repertory. From 2006 to 2012, he was the director of two of Croatia's prominent summer festivals, the Split Summer Festival (2006-2009) and then the Dubrovnik Summer Festival. Repušic became Kapellmeister of the Hanover State Opera in 2010, leading performances of major German operas, and in 2012, he assumed the same position at the Staatsoper Berlin. Repušic has had a notable career as an orchestral conductor as well, serving since 2005 as the conductor of the Zadar Chamber Orchestra. As a guest, he has led all the major Croatian orchestras, as well as the Giuseppe Verdi Symphony Orchestra in Milan, the Prague Symphony Orchestra, and the Slovenian Philharmonic, among others. He has also had an ongoing relationship with the Munich Radio Orchestra.
With that group, Repušic has made several recordings on the BR Klassik label, including, in 2019, Fuoco di Gioia!: Berühmte Opernchöre. That year he backed Emmanuel Pahud in a flute recital on Warner Classics. Repušic has been a member of the faculty at the Academy of Arts of the University of Split since 2016. ~ James Manheim, Rovi