Leipsic was selected by the Nashville Predators in the third round (No. 89) in the 2012 NHL Draft after he had 58 points (28 goals, 30 assists) in 65 games in his second season with Portland of the Western Hockey League.

Leipsic played two more seasons with Portland and had 211 points (88 goals, 123 assists) in 128 games, including 120 points (49 goals, 71 assists) in 2012-13, when he won the Bob Clarke Trophy as the WHL's top scorer and the Canadian Hockey League Top Scorer Award.

On May 23, 2013, the Predators signed Leipsic to a three-year, entry-level contract.

He began his first professional season with Milwaukee of the American Hockey League, where he was fourth in scoring with 35 points (seven goals, 28 assists) despite playing 47 games. On Feb. 15, 2015, he was acquired by the Toronto Maple Leafs in a trade with the Predators. He was assigned to Toronto of the AHL and had 19 points (seven goals, 12 assists) in 27 games.

In 2015-16, Leipsic was third on Toronto in scoring with 54 points (20 goals, 34 assists) in 65 games and was called up on an emergency basis by the Maple Leafs on Feb. 13, 2016. He made his NHL debut that night against the Vancouver Canucks and scored a goal in the Maple Leafs' 5-2 win. Leipsic had three points (one goal, two assists) in six games with the Maple Leafs.

After spending the 2016-17 season with Toronto of the AHL, finishing with 51 points (18 goals, 33 assists) in 49 games, Leipsic was left unprotected in the 2017 NHL Expansion Draft and was selected by the Vegas Golden Knights, who signed him to a two-year contract on July 15, 2017.

Leipsic had 13 points (two goals, 11 assists) in 44 games for Vegas before being acquired by the Canucks in a trade with the Golden Knights on Feb. 26, 2018. In 14 games with Vancouver, he had nine points (three goals, six assists).