One year after commencing his studies at the Béla Bartók Conservatory in 2008 as a student of Mária Fekete, Zoltán Daragó became the first singer to win admittance to the Ferenc Liszt Academy of Music's special programme for young talents, where he studied under Éva Marton. After graduating from the conservatory, he spent a year in The Hague at the Royal Conservatory there, where his teacher was Gerda van Zelm. In 2014, he was again enrolled at the Liszt Academy, studying with Júlia Pászthy.

Zoltán made his debut with the Hungarian State Opera in 2015 in the role of Blindleech in Zsófia Tallér's opera Leander and Linseed, the youngest
opera singer in the company at just twenty-two. He has sung five roles in thirty-one performances during three seasons with the Hungarian State Opera House while completing his undergraduate degree at the Liszt Academy, where he graduated in the spring of 2017.