[1] On July 9, 2016, Gauthier was signed to his first NHL deal in agreeing to a three-year, entry-level contract with the Carolina Hurricanes.

[5] During the 2019–20 season, on February 18, 2020, Gauthier was traded by the Hurricanes to the New York Rangers in exchange for defenceman Joey Keane.

[11] In his debut with the Senators he played on a line with Parker Kelly and Ridly Greig against the Boston Bruins on February 20.

[13] As a free agent from the Senators, Gauthier was signed to a two-year, $1.575 million contract with the New York Islanders on July 5, 2023.

[17] On December 1, 2015, Gauthier was invited to the Team Canada selection camp for the 2016 World Junior Hockey Championships.

[20] Gauthier was again invited to Team Canada's selection camp for the 2017 World Junior Hockey Championships.