[1] Ivan moved to North America in 2019, playing the 2019–20 season with the Cape Breton Eagles of the Quebec Maritimes Junior Hockey League (QMJHL).

[4] He turned professional in 2023, signing a contract with the Colorado Eagles of the American Hockey League (AHL).

[1] On 5 March 2024, he signed a two-year contract with the Colorado Avalanche of the National Hockey League (NHL).

[11] Ivan scored his first NHL goal on 24 October 2024, assisted by Nathan MacKinnon and Casey Mittelstadt.

[1] He competed at the Hlinka Gretzky Cup in 2019–20 and later for the Czech U20 national team at the 2022 World Junior Ice Hockey Championships.