After playing his draft-eligible season with the Lincoln Stars of the United States Hockey League (USHL) and recording 18 goals and 39 points in 51 games, Cotter was selected in the fourth round, 115th overall, by the Vegas Golden Knights at the 2018 NHL entry draft.

[1] Although Cotter began the 2018–19 season with Western Michigan University, he left in November 2018 after appearing in eight games and signed with the London Knights of the Ontario Hockey League (OHL), in part because he believed going the major junior route would help him secure an entry-level contract with Vegas.

[2] During the 2021–22 season, Cotter was recalled by the Golden Knights and made his NHL debut on November 9, 2021, against the Seattle Kraken.

[4] Cotter, as a rookie, spent the entire 2022–23 season, on Vegas' roster, ultimately playing 55 regular-season games and recording 13 goals.

[5] On June 29, 2024, Cotter was traded by the Golden Knights to the New Jersey Devils in exchange for Alexander Holtz and Akira Schmid.