O'Connor first played as a bantam and midget within the Calgary Royals organization of the Alberta Midget Hockey League. Opting to pursue a collegiate career, O'Connor was selected with the 194th overall pick by the Sioux Falls Stampede in the 2013 United States Hockey LeagueEntry Draft. During first junior season with the Stampede in the 2013–14 season, O'Connor committed to the University of Denver of the National Collegiate Hockey Conference. As a 17-year-old with Sioux Falls, O'Connor was placed on the checking line and recorded 3 goals and 10 points in 59 games. In the following 2014–15 season, O'Connor was named captain of the Stampede and continued his development by increasing his scoring presence in posting 16 goals and 36 points in 58 regular season games. In the postseason, he contributed 10 points in 12 games for Sioux Falls to help capture the Clark Cup. Embarking on his collegiate career with the Denver Pioneers in the 2015–16 season, O'Connor appeared in 23 games for two goals and two assists as a freshman. In the following 2016–17 season, he became a fixture among the Pioneers checking line, registering 7 goals and 18 points while appearing in all 44 games to help Denver claim the 2017 national championship. In his junior season in 2017–18, O'Connor again appeared every game with the Pioneers, posting a season-best 21 points while leading the Pioneers with two short-handed goals through 41 games. He helped the Pioneers claim the NCHC championship and was named to the All-Tournament Team. Named as a two-time All-Academic in the NCHC, O'Connor was selected as captain of the Pioneers for his senior season on June 7, 2018.
Professional
At the conclusion of his junior season and following the 2018 NHL Entry Draft, O'Connor was invited to attend the Colorado Avalanche development camp. On July 24, 2018, O'Connor forwent his senior season as captain with the Pioneers in agreeing to a two-year, entry-level contract as an undrafted free agent with the Avalanche. In his first training camp and pre-season with the Avalanche, O'Connor impressed with his speed and was among the last cuts assigned to begin 2018–19 season with the minor league affiliate, the Colorado Eagles, for their inaugural season in the American Hockey League. He made his professional debut in the Eagles home opening night game against the Chicago Wolves on October 5, 2018. He registered his first goal and point in his third game, notching the game-winner in the Eagles' first victory in the AHL in a 2–1 win over the San Antonio Rampage on October 12, 2018. O'Connor was making a quick transition to the professional level contributing offensively with the Eagles, placing second on the club with nine goals before he received his first call-up to the Avalanche on December 31, 2018. He immediately made his NHL debut with the Avalanche, skating on the fourth-line alongside, Gabriel Bourque and Sheldon Dries, in a 3–2 overtime defeat to the Los Angeles Kings. He recorded his first NHL goal in a 4-1 win against the Edmonton Oilers on November 27, 2019.