[2] In sixth grade, Gaudette was admitted to Thayer Academy to join their hockey team, and his family moved from Taunton, Massachusetts, to Braintree to accommodate his commute to and from the skating rink.

Although he lost most of his first two high school ice hockey seasons to injuries, as a junior, Gaudette recorded 67 points in 27 games.

[7] Skating as a freshman for the Cedar Rapids RoughRiders of the United States Hockey League, Gaudette scored 30 points in 41 games.

In 2016, he tallied a goal and an assist to beat fellow Canucks prospect Thatcher Demko of Boston College to propel Northeastern to the Hockey East Championship.

[10] Two years after being drafted in the fifth round, he was called a "first-rate prospect," ranking first in NCAA power-play goals with 14 and third in points after 31 games and in the top 10 nationally.

"[13] During the 2017–18 season Gaudette recorded career highs in goals and assists while leading the Huskies to their first Beanpot championship in 30 years.

After attending Canucks training camp prior to the 2018–19 season, Gaudette was reassigned to their American Hockey League (AHL) affiliate, the Utica Comets.

[20] However, his stint in the AHL did not last long as he was called up to the NHL on October 15 after playing in four games for the Comets, where he tallied two goals and two assists.

[23] Despite being expected to spend most of the season developing in Utica, injuries to Canucks centers resulted in Gaudette appearing in 56 games for Vancouver.

[24][25] Gaudette ended his rookie season with five goals and seven assists, generally playing center on Vancouver's third line.

[26] After being recalled on October 27,[27] Gaudette responded by scoring six goals and ten points in November 2019, solidifying his spot in the lineup.

[33] As a free agent, after not being tendered a qualifying offer from the Senators, Gaudette was signed a one-year, $750,000 contract with the Toronto Maple Leafs on July 13, 2022.

[34] Gaudette cleared waivers and was assigned to the Maple Leafs AHL affiliate, the Toronto Marlies on October 13, 2022.