Terry, a fifth-round pick (No. 148) in the 2015 NHL Draft, made his NHL debut with the Anaheim Ducks on March 27, 2018, after a decorated amateur career that included three seasons at the University of Denver. The 20-year-old forward had three shots on goal in two games.

Terry starred with the USA Hockey National Team Development Program, and had five points (three goals, two assists) to help the United States win the 2015 IIHF World Under-18 Championship.

He burst into international prominence at the 2017 IIHF World Junior Championship. Against Russia in the semifinals he scored three times in the shootout, including the game-deciding goal in the seventh round, in a 3-2 win. He followed that by scoring the only goal of the shootout to give the U.S. a 5-4 win against Canada in the first-place game.

Terry finished the 2016-17 season leading Denver with 45 points (22 goals, 23 assists). He helped Denver reach the final of the Frozen Four and had two assists, including one on the game-winning goal, in a 3-2 win against Minnesota Duluth in the championship game.

In 2017-18, his third season at Denver, Terry had 48 points (14 goals, 34 assists) in 39 games. He also had five assists in five games for the United States at the 2018 PyeongChang Olympics.

Terry's 16-game point streak (12 goals, 10 assists) achieved during the 2021-22 season (Oct. 18 to Nov. 18) made him the youngest player (24 years, 67 days) in Ducks history with a run of at least 15 games. Two Anaheim skaters have had longer point streaks: Corey Perry (19 games in 2009-10) and Teemu Selanne (17 in 1998-99). Terry was the youngest NHL player at that time with points in 15 consecutive games since Patrik Laine (19 years, 333 days) had a 15-game point streak for the Winnipeg Jets from Feb. 16 to March 18, 2019.