He had previously played in the National Hockey League (NHL) within the Toronto Maple Leafs, Vancouver Canucks, Calgary Flames, Carolina Hurricanes and St. Louis Blues organization.

[3] Growing up, Leivo played with the Barrie Colts U18 AAA team before being drafted by the Sudbury Wolves of the Ontario Hockey League (OHL).

[16] He finished the month of October by earning the Wolves' Three-Star Award after scoring 10 goals and six assists, including two winners, for 16 points through 16 games.

On January 8, 2013, Leivo was traded in a multi-player deal to the Kitchener Rangers alongside Frank Corrado, Joel Vienneau, and various draft picks.

[21] However, in the early stages of the 2013–14 season, on October 10, 2013, Leivo made his NHL debut with the Toronto Maple Leafs in a 4–0 win over the Nashville Predators.

[26] Following his first full professional season, Leivo participated in the Leafs Development and training camp playing alongside Nazem Kadri and William Nylander.

[30] Throughout his time with the Marlies, Leivo played on both left and right wings with various linemates including Trevor Smith, Spencer Abbott, Greg McKegg, and Sam Carrick.

[31] Following the AHL All-Star game, Leivo returned to the NHL lineup due to various injuries on the Maple Leaf's main roster.

[40] After suffering an injury during training camp, Leivo went pointless in five games with the Marlies on a conditioning stint[41] before being declared unfit to play by the Maple Leafs.

[42] After making his season debut, Leivo failed to become a mainstay in the Leafs lineup until Mitch Marner suffered an injury in mid-February.

[43] He was then slotted into the Leafs' home-ice shutdown line alongside Leo Komarov and Nazem Kadri where he began producing at a rapid rate.

[47] His agent Ian Pulver stated that Leivo wished to stay in Toronto and fight for time on ice rather than take a chance with free agency.

[51] After appearing in a career-high 27 games for the Leafs during the 2018–19 season, Leivo was traded to the Vancouver Canucks in exchange for Michael Carcone on December 3, 2018.

[55] As he continued to play on Vancouver's top offensive line, head coach Travis Green praised Leivo's size, strength, and "ability to hang on to the puck down low.

[59] Although Leivo spent the majority of the previous season with Pettersson and Boeser, he logged at least 10 minutes of 5-on-5 ice time with nine different line combinations throughout October and November.

[62] As a free agent from the Canucks after parts of two seasons with the club, Leivo opted to remain in Western Canada by signing a one-year, $875,000 contract with the Calgary Flames on October 24, 2020.

[63] He stated that one of the reasons he signed with the Flames was due to his familiarity with numerous players on the team, specifically Sean Monahan, Mark Giordano, Jacob Markström, and Christopher Tanev.

"[65] In the Flames home opener against his former team, the Canucks, Leivo played on their top line alongside Monahan and Johnny Gaudreau.

[74] During his time with the Wolves in December, Leivo accumulated a league-leading 14 points through six games to help Chicago post its first perfect record for a month in its franchise history.

[76] As the season continued, Leivo and teammates Stefan Noesen and Andrew Poturalski played a vital role in helping the team qualify for the 2022 Calder Cup playoffs.

During the post-season, Leivo led all AHL skaters with 20 points through 13 games to help the Wolves advance to the Calder Cup Finals.

[77] As the Wolves beat the Springfield Thunderbirds in the Finals, Leivo won the Jack A. Butterfield Trophy as the Most Valuable Player of the Calder Cup Playoffs.