Connor was born and raised in New Jersey where he began his hockey journey that eventually led him to the US National Development Team. As a member of the National Team, Connor helped the US win a silver medal at the 2013 World Under-18 Championship and later that year was drafted in the 5th round by the Arizona Coyotes. The following season, Connor began his freshman season with Quinnipiac University. He went on to play four seasons with Quinnipiac and was named to the ECAC Hockey All-Academic Team during all four of his seasons. Connor was named team captain in his junior season and at the conclusion of the season was also named to the ECAC All-Tournament team, NCAA East All-Frozen Four Team and honored as the ECAC Hockey Tournament Most Outstanding Player. Following his college career, Connor signed a contract with the Providence Bruins of the AHL. The following season he was signed by the Boston Bruins and made his NHL debut on November 18, 2018. He registered his first point later that season in a game against the St. Louis Blues. In the summer of 2019, Connor signed a three-year extension with the Boston Bruins and has remained a member of the team since.