Jet Greaves was born just outside of Toronto in Cambridge,Ontario and grew up playing for the Cambridge Hawks.

He was drafted by the Barrie Colts in the third round of the 2017 OHL draft and made his debut for the Colts in 2018-19. In his rookie season, Jet was named to the OHL’s First-All-Rookie Team finishing the year with a 0.911 save percentage which ranked third in the OHL. Jet returned to Barrie in 2019-20 suiting up for 33 games before not playing the entire 2020-21 season as a result of the Covid-19 pandemic. In 2021-22, Jet made his pro debut with the Kalamazoo Wings of the ECHL. After suiting up in 15 games, he was called up to the AHL affiliate Cleveland Monsters where he played in 29 AHL games posting a 0.905 save percentage and a 2.84 goals against average.

As a result of his impressive season, the Columbus Blue Jackets signed him to a 3-year entry-level contract beginning in 2022-23. Jet played in 43 games for Cleveland in 2022-23 and made his NHL debut with the Columbus Blue Jackets on April 4, 2024 against his hometown Toronto Maple Leafs. Despite losing 4-2, Jet set a Blue Jackets debut record making 46 saves and became just the ninth goalie in league history to register 45 or more saves in an NHL debut. Jet split time between the AHL and NHL clubs in 2023-24. He played in 9 NHL games for Columbus recording a team leading 0.908 save percentage. While with Cleveland, Jet played in 46 games recording 30 wins and led the AHL playoffs with a 0.926 save percentage.