In the 2012–13 season, Morrissey led Prince Albert defenceman in points, scoring 15 goals and 32 assists to go with a +14 plus-minus rating and 91 penalty minutes. The Raiders finished with a winning record for the first time since 2003–04.
In the subsequent off-season, Morrissey was drafted by the Winnipeg Jets in the first round, 13th overall, of the 2013 NHL Entry Draft. Prior to the beginning of the 2013–14 season, Morrissey was named captain of the Raiders.[3] On October 3, 2013, the Winnipeg Jets signed him to three-year, two-way contract,[4] although he returned to Prince Albert for the season. He finished as the second-leading scorer in the WHL during the 2013–14 season, recording 28 goals and 45 assists (73 points) in 59 regular season games, along with a +6 plus-minus rating and 59 penalty minutes. The Raiders were fourth in the East Division before being swept by the eventual 2014 Memorial Cup champions, the Edmonton Oil Kings, in the first round.
Morrissey scored his first career NHL goal on November 15, 2016, in a 4–0 win over the Chicago Blackhawks.[9] He finished his first full season with the Jets with 6 goals and 20 points in 82 games. During his second season with the Jets, Morrissey recorded 26 points in 81 games to help the Jets qualify for the 2018 Stanley Cup playoffs. During the first round, Morrissey was suspended one game for cross checking Eric Staal of the Minnesota Wild.[10]
On September 12, 2019, Morrissey signed an 8-year, $50 million extension with the Jets, carrying an annual average of $6.25 million.[11] Later, on October 1, 2019, just prior to the start of the 2019–20 NHL season Morrissey was named an alternate captain of the Jets.