[2] While growing up alongside three other siblings,[3] Connor began playing youth hockey in the Belle Tire organization in Metro Detroit.

He joined Tyler Motte as the only player in the Big Ten to earn First Star of the Week honors three times this season.

Connor extended his Red Berenson-era (since 1984) Michigan record point streak to 23 games with four goals in two wins against Penn State.

[30] On April 11, 2016, Connor left the University of Michigan and signed a three-year, two-way contract with the Winnipeg Jets worth an average annual value of $1.775 million.

[31] He made his NHL debut on October 13, playing alongside Mathieu Perreault and fellow rookie Patrik Laine.

[33] However, after Laine suffered an injury in the season opener, Connor and Perreault gained Drew Stafford as their second line right winger.

Connor was subsequently placed on injured reserve and the Jets called up Chase De Leo from their American Hockey League affiliate, the Manitoba Moose.

[45] Upon being recalled, Connor scored the game-tying goal in the Jets' final game of the regular season to lift the team 2–1 over the Nashville Predators.

By winning the game, the Jets secured the second Wild Card spot in the Western Conference for the 2017 Stanley Cup playoffs.

[49] He reunited with Laine on the Jets' second line, along with Bryan Little, for his season debut against the Columbus Blue Jackets on October 16.

[53] He remained on a line with Scheifele and Wheeler throughout the first half of the season and recorded nine goals and eight assists while averaging 17:50 in ice time.

[58] While climbing the ranks, Connor also became the second rookie in NHL history to score two regular-season overtime goals in consecutive games.

[59] On March 25, Connor recorded a goal and two assists to help the Jets clinch a spot in the 2018 Stanley Cup playoffs.

[61] On April 3, Connor scored another overtime winner and added two assists to help the Jets become the 80th team in NHL history to win 50 games in a season.

[63] Connor was one of eight Jets players to make their NHL postseason debut in Game 1 of the Western Conference First Round against the Minnesota Wild.

[65] During their series, Connor tallied two assists in five games as the Jets beat the Wild and moved on to the second round against the Nashville Predators.

[68] Wheeler and Connor each recorded two assists to help the Jets qualify for the Western Conference Final against the Vegas Golden Knights.

[71] Connor ranked fourth in Calder Memorial Trophy voting, which was ultimately won by New York Islanders forward Mathew Barzal.

[84] On March 23, Connor scored his first career NHL hat-trick, and added an assist, in a 5–0 win over the Nashville Predators.

As the negotiations bled into training camp, Connor began skating at the University of Michigan prior to a deal being signed.

[87] On September 28, after missing most of the preseason, Connor signed a seven-year, $50 million contract extension to remain with the Jets.

[88] Upon joining the Jets for their season opener against the New York Rangers, Connor was reunited with Mark Scheifele and Blake Wheeler on the top line.

[93] While playing alongside Scheifele and Laine, Connor helped the Jets improve to a winning 17–10–1 record through the start of December.

[99] When the NHL paused play due to the COVID-19 pandemic in March, Connor had already set new career highs in goals, assists, and points.

He finished the shortened regular season with 38 goals and 35 assists to tie Scheifele for the team's scoring lead with 73 points.

[100] Beyond accumulating points, Connor also finished with the highest average ice-time among left wingers and ranked 10th in the NHL with 239 shots on goal.

During the tournament, he scored four goals and added two assists to help Team USA clinch a gold medal.

[105] After earning a silver medal, Connor represented Team USA a second time in 2013 while playing in the 2013 World Junior A Challenge.

[108] Following this, he represented Team USA at the 2014 World Junior A Challenge, where he recorded one goal and one assist in four games to win a gold medal.

[109] While attending the University of Michigan, Connor was chosen to represent the United States men's national ice hockey team for the first time at the 2016 IIHF World Championship alongside UMich line-mates J. T. Compher and Tyler Motte.