[6] However, after playing two games at the NHL level, he was reassigned to the Rangers' American Hockey League (AHL) affiliate, the Hartford Wolf Pack.

[11] On 2 November 2023, during a 2–1 victory against the Carolina Hurricanes, Chytil suffered the fourth concussion of his career and was placed on injured reserve.

[12] On 28 January 2024, he was ruled out for the rest of the 2023–24 regular season after suffering a setback during practice two days earlier.

[13][14] Chytil returned to play on 9 May, in game 3 of the second round of the 2024 Stanley Cup playoffs in a 3–2 overtime win over the Carolina Hurricanes.

[16] Chytil was a member of the Czech Republic under-18 team that won gold at the 2016 Ivan Hlinka Memorial Tournament.