[2] He was born into a hockey-involved family as his father played four seasons in the Western Hockey League[3] while his uncle was a radio host for The Sports Network until TSN 1260 was shut down in June 2023.

[3] While playing for the Leduc Oil Kings Bantam in the 2013–14 season, Gregor led the AMHL with 21 goals and 30 points through 35 games.

[3] Gregor was selected in the third round, 55th overall, by the Victoria Royals in the 2013 WHL bantam draft,[8] the same city that his father played in.

On January 6, 2014, the Royals traded Gregor's rights to the Moose Jaw Warriors in exchange for Travis Brown.

[22] He subsequently joined the team's American Hockey League (AHL) affiliate, the San Jose Barracuda, skating in one postseason game.

Gregor was not tendered a qualifying offer by the Sharks following the conclusion of the season, making him an unrestricted free agent.

[29] On September 6, 2023, Gregor agreed to a professional tryout offer with the Toronto Maple Leafs to attend their training camp.

[31] In his first game for the team on October 11, Gregor scored the Maple Leafs' first goal of the season in an eventual 6–5 win over the Montreal Canadiens.

[32] On March 24, 2024, Gregor suffered a high stick to the face by Washington Capitals forward Tom Wilson.

[34] He made his Stanley Cup playoffs debut in Game 6 of the Maple Leafs' first round series against the Boston Bruins.