Drury was given a new hockey home when he was traded to the Colorado Avalanche on Jan. 24, 2025, in a three-team deal involving the Carolina Hurricanes and Chicago Blackhawks that sent Mikko Rantanen and Taylor Hall to Carolina. He scored his first goal with the Avalanche in a 5-4 win at the New York Rangers two days later.

Drury is a native of New York City. His father, Ted Drury, played 414 NHL games for the Calgary Flames, Hartford Whalers, Ottawa Senators, Mighty Ducks of Anaheim, Columbus Blue Jackets and New York Islanders. Chris Drury, Jack's uncle, played 892 games and won the Stanley Cup with the 2000-01 Avalanche. The Hurricanes selected Jack in the second round (No. 42) of the 2018 NHL Draft and signed him to his entry-level contract July 7, 2021, following his first professional season with Vaxjo of the Swedish Hockey League.

Drury had 30 points (10 goals, 20 assists) in 41 games for the Lakers in 2020-21 and was named one of three finalists for the SHL's Rookie of the Year award. He was second in the playoffs with 11 points (five goals, six assists) in 14 games to help Vaxjo become league champions. This after he played two seasons at Harvard, where we had 63 points (29 goals, 34 assists) in 60 games. He played for the United States at the 2019 IIHF World Junior Championship (silver) and 2020 World Juniors (sixth place), and won bronze at the 2021 IIHF World Championship.