[8] In the leadup to the 2022 NHL entry draft, Jiříček was considered a top prospect, and for much of the year there was debate as to whether he or Slovak Šimon Nemec would be the first defenceman taken.

[1] Jiříček began his North American professional career playing with the Cleveland Monsters, the Blue Jackets' AHL affiliate.

[14] Jiříček was initially named as the Monsters' representative to the 2023 AHL All-Star Classic, but he subsequently was unavailable to participate and was replaced by teammate Jake Christiansen.

[24][25] However, he suffered an injury in his first game after a knee-on-knee collision with Team Canada forward Will Cuylle, and was forced to withdraw from the tournament.

[26] Jiříček returned to the ice for the 2022 IIHF World Championship, where he played five games in his debut with the senior national team, before a planned withdrawal to avoid overtaxing his knee.

[27] The tournament was an international breakout for Jiříček, who was cited as a central player in Czechia's deep run to the event final, where they ultimately took the silver medal after a loss to Canada.