Peeke played for the Notre Dame Fighting Irish men's ice hockey team for three seasons while majoring in management consulting. Prior to joining the team, he was drafted 34th overall by the Columbus Blue Jackets in the 2016 NHL Entry Draft, becoming the 13th American selected in the draft. Upon joining the Fighting Irish for the 2016–17 season, Peeke recorded 14 points in 40 games as the program transitioned from the Hockey East to Big Ten Conference. Before and during his rookie season, Peeke was encouraged by Blue Jackets management to work on his skating, shot, and release. Following his rookie season, he earned praise from the Jackets development coach Chris Clark for exceeding their expectations.
