[10] Drysdale joined the Otters for the 2018–19 OHL season, making his junior ice hockey debut with two assists in Erie's season-opening 12–1 win over the Flint Firebirds.

[13] Drysdale's overtime goal against the London Knights on February 15, 2019, was his 29th point of the season, breaking Travis Dermott's franchise record for a rookie defenceman.

[25] The Anaheim Ducks selected Drysdale sixth overall in the 2020 NHL entry draft,[26] and he signed a three-year entry-level contract with the team on November 7.

[27] When the 2020–21 NHL season began in January, the Ducks assigned Drysdale to the San Diego Gulls, their American Hockey League (AHL) affiliate.

[28] After recording ten points in his first 14 AHL games and being named the league's Rookie of the Month for February, Drysdale was promoted to Anaheim's taxi squad in March.

[35] As the season progressed, Drysdale struggled to balance his offensive output with maintaining his defence, telling reporters that it was "just a matter of noticing when and where you are in the game and making the smart play".

[38] The Ducks underwent major line-up changes prior to the 2022–23 season, and Drysdale opened the year on the second defensive pair alongside Dmitry Kulikov.

[39] On October 22, in the second period of a 4–0 loss to the Vegas Golden Knights, Drysdale took a hit from William Carrier behind Anaheim's net and left the game.

[41][42] A restricted free agent prior to the 2023–24 season, Drysdale's contract negotiations extended throughout the offseason, forcing him to miss part of training camp.

[47] Flyers coach John Tortorella praised Drysdale's skating ability and told reporters that he hoped for more offensive production from the defenceman, who joined Philadelphia's league-worst power play unit.

[51][52] Drysdale made his first international tournament appearance at the 2018 World U-17 Hockey Challenge in New Brunswick, where he served as captain of team Canada Black.

[34][54] Subsequently, Drysdale appeared with the Canada men's national under-18 ice hockey team at the 2019 IIHF World U18 Championships in Sweden,[55] where he recorded two assists in seven games en route to a fourth-place finish.

[34] In 2020, at the age of 17 years and eight months, Drysdale became the youngest defenceman to appear on the Canada men's national junior ice hockey team since Jay Bouwmeester in 2001.