After a successful stint with Ulsan Hyundai, Oršić was bought in 2018 by Croatian giants and his local club Dinamo Zagreb, whom he had supported since childhood.

He played for Ulsan for one and a half years, during which he won a Korean FA Cup title, before returning to Croatia and signing for Dinamo Zagreb in the 2018 summer transfer window.

[21] On 9 December 2021, he scored the only goal in the 1–0 away victory over West Ham United in the Europa League group stage, sending Dinamo to the knockout round play-offs.

[22] On 6 September 2022, Oršić scored the first goal of the 2022–23 Champions League group stages in a famous 1–0 victory for Dinamo against Chelsea at the Maksimir.

[27] On 11 January, Oršić made his debut in a 2–0 quarter-final EFL Cup victory against Manchester City, replacing Adam Armstrong in the 83rd minute.

[28] Later that month, on 21 January, Oršić made his only Premier League appearance in a 1–0 home defeat to Aston Villa after he replaced Armstrong in the 84th minute.

[35] Oršić made his international debut for Croatia on 9 September 2019 in a Euro 2020 qualifying match against Azerbaijan in Baku that ended as a 1–1 draw, coming on as a substitute for Ante Rebić in the 86th minute.

[40] On 27 November, in the 4–1 group stage victory over Canada, Oršić provided Lovro Majer with an assist for Croatia's fourth goal.

[41] On 9 December, in the quarter-final against Brazil, Oršić provided Bruno Petković with the assist for Croatia's extra time equaliser, taking the match to a penalty shootout.

Oršić would score his penalty in the shootout, the final Croatian spot-kick before Marquinhos' miss, which sent Croatia to the semi-finals for the second consecutive World Cup.