Zvonarek joined the youth academy of Slaven Belupo in 2016, at the age of 11,[2] coming from Mladost Prelog.[3] He made his professional debut with Slaven in a 2–0 Prva HNL loss to Rijeka on 12 May 2021.[4] He scored the only goal in his second appearance, a 1–0 win over Varaždin on 22 May 2021; at 16 years and 14 days old, he became the youngest ever scorer in the Prva HNL taking the record from Alen Halilović.[5]
Bayern Munich
On 10 September 2021, Zvonarek signed a long-term contract with German club Bayern Munich for a reported fee of €1,800,000,[6] although he remained with Slaven Belupo until the end of the 2021–22 season, he would join Bayern Munich II afterwards for further development.[7]
On 1 November 2023, Zvonarek received his first call-up for the Bayern Munich senior team as an unused substitute in the second round DFB-Pokal away 2–1 loss match against 1. FC Saarbrücken.[9]
He made his debut with the Bayern Munich senior team on 27 January 2024, coming off the bench for a Bundesliga 3–2 away win match against FC Augsburg.[10] Later that year, on 12 May, he netted his first Bundesliga goal during his inaugural start in a 2–0 victory against VfL Wolfsburg.[11] Three days later, he signed his first professional contract with the club until 2027.[12]
From 2019 until 2020, Zvonarek has been part of Croatia at youth international level, respectively has been part of the U15 and U16 teams and he with these teams played nine matches and scored two goals.[14]