[6] Growing up in New York, Zegras played bantam major ice hockey with the Mid Fairfield Rangers before joining the Avon Old Farms school's Winged Beavers of the Founders League (USHS).

[5] Zegras joined the USNTDP under-17 team for their 2017–18 season in the United States Hockey League (USHL), where he recorded 20 goals and 39 assists for 59 points.

[4] In spite of his draft selection, Zegras kept his commitment to play college ice hockey for Boston University.

[8] Zegras played for the Boston University Terriers men's ice hockey team in the 2019–20 NCAA season, competing in 33 games where he finished tied for third among Division I freshmen in points with 36.

[11] Following the signing, Zegras was re-assigned to their American Hockey League (AHL) affiliate, the San Diego Gulls, to play out the remainder of the 2020–21 season.

When speaking of the re-assignment, executive vice president and general manager Bob Murray stated: "He's ahead of our scheduled progression, and as a result, we are moving him to center ice effective immediately.

"[17] Upon returning to the AHL, Zegras made the transition from left wing to center, which resulted in an increased offensive output.

[18] During training camp prior to the 2021–22 season, Zegras continued to play the role of center[16] and was named to their opening night roster.

[27] The following season, Zegras led the team in all statistical categories despite missing the playoffs, while recording a career-high 65 points and sharing the number of goals scored (23) with Troy Terry.