Drysdale was traded to the Philadelphia Flyers with a second-round pick in the 2025 NHL Draft by the Anaheim Ducks for Cutter Gauthier on Jan. 8, 2024. He scored in his 200th NHL game, a 3-1 Flyers loss to the New Jersey Devils in Philadelphia on March 9, 2025.

Though the defenseman missed the final 74 games of the 2022-23 season with a torn labrum in his left shoulder, he became the fourth Ducks rookie at his position to have at least 30 points with 32 (four goals, 28 assists) in 81 games of the 2021-22 season, joining Hampus Lindholm (2013-14), Cam Fowler (2010-11) and Francois Beauchemin (2005-06). Drysdale was the only defenseman from his draft class to play an NHL game in 2020-21. His goal and assist against the Arizona Coyotes on March 18, 2021, made him the third at his position in NHL history with multiple points in his NHL debut at age 18 or younger.

The Ducks selected Drysdale with the No. 6 pick in the 2020 NHL Draft after he was an Ontario Hockey League First-Team All Star for Erie in 2019-20 with 47 points (nine goals, 38 assists) in 49 games during his second season. He was 10th among OHL defensemen in points per game (.96) and led Erie defensemen in goals, assists, points, power-play assists (19) and power-play goals (three).

Drysdale helped Canada win the 2020 IIHF World Junior Championship with three points (one goal, two assists) in seven games. At 17 years, eight months, Drysdale became the youngest defensemen since 2001 to play for Canada at World Juniors since Jay Bouwmeester (17 years, three months), and the sixth-youngest Canada-born defensemen in tournament history.