Bear was drafted in the fifth round in the
2015 NHL entry draft by the
Edmonton Oilers from the
Seattle Thunderbirds of the
Western Hockey League (WHL). He was signed to a three-year, entry-level contract with the Oilers on July 2, 2016. Bear made his NHL debut on March 1, 2018, in a game against the
Nashville Predators. He recorded his first NHL goal in a 5–4 overtime loss to the
Anaheim Ducks on March 25, 2018. Bear was the first player to wear a jersey with his name written in
Cree syllabics (;
Maskwa) during an exhibition match against the
Calgary Flames on July 28, 2020. On December 28, 2020, Bear signed a two-year, $4 million contract extension with the Oilers. After his fourth year within the Oilers organization, Bear was traded to the
Carolina Hurricanes in exchange for
Warren Foegele on July 28, 2021. In the following
2021–22 season, Bear tied a career-high with five goals and added nine assists for 14 points through 58 regular season games. Struggling to fully adjust to the Hurricanes' system, Bear was a
healthy scratch through two rounds of the playoffs. As a restricted free agent in the off-season, Bear was re-signed by the Hurricanes to a one-year, $2.2million contract on July28, 2022. Beginning the
2022–23 season as a healthy scratch, Bear was traded by the Hurricanes alongside
Lane Pederson to the
Vancouver Canucks in exchange for a 2023 fifth-round pick. In 2023, Bear joined the NHL Player Inclusion Coalition. After injuring his shoulder while playing in the
2023 IIHF World Championship, Bear had to rest for six months after receiving surgery. Following the surgery, he was not issued a
qualifying offer by the Canucks. As Bear emerged from his recovery as an
unrestricted free agent, Canucks insider Chris Johnston reported that, alongside the Canucks, the
Washington Capitals and the
Toronto Maple Leafs expressed interest in signing him. An unnamed source told
Postmedia that the Canucks' available
cap space stopped them from re-signing Bear for the
2023–24 season. Bear signed a two-year, $4.125million contract with the Washington Capitals on December28, 2023. He debuted for the Capitals on December30, 2023, against the
Nashville Predators. After playing 24 games with Washington, Bear entered the NHL/NHLPA player assistance program in March 2024. He was cleared to return to the team at the end of April. On October 3, 2024, the Capitals placed Bear on waivers. After clearing waivers, Bear began the
2024–25 season playing with the Capitals’ AHL affiliate, the
Hershey Bears. Appearing in 62 games, he led Hershey in scoring with 46 points, and tied for the league lead in
plus minus rating (+33). In recognition of his play, Bear was named to the Second All-Star Team. Having left the Capitals as a free agent, Bear was signed to a one-year, two-way contract with the New York Islanders for the season on July 1, 2025. ==International play==