[4][3] In the 2022–23 season, Reinbacher established himself a regular on Kloten's blueline, attracting attention for doing so as an 18-year-old player, and seeing his average ice time rise from six minutes per game to over 20.

[6] By November 2022, he was receiving attention from major North American publications, with The Hockey News naming him to their "All-Sleeper Squad" of players who should be considered for the first round.

[8][9][10][11] At the draft, Reinbacher was selected fifth overall by the Montreal Canadiens, with team general manager Kent Hughes describing him as "a diamond in the rough with a lot of potential.

[4] The Canadiens' decision was controversial due to their passing over Matvei Michkov, considered by many to be the most talented player still available at the time, who was subsequently taken by the Philadelphia Flyers.

[16][17] After what was generally considered a positive appearance at the Canadiens' training camp in the autumn of 2023, he was sent back to EHC Kloten for the 2023–24 NL season.

[20] Following the end of the NL season, he was assigned to the Laval Rocket, the Canadiens' American Hockey League (AHL) affiliate, on 18 March 2024.