During the 2020–21 season, his junior year, he recorded five goals and seven assists in 29 games. His five goals were tied with Nick Leivermann and Michigan's Nick Blankenburg for the most by a Big Ten defenseman.[4] Following the season, he was named to the All-Big Ten Second Team.[6] During the 2021–22 season, his senior year, he recorded a career-high seven goals and 20 assists in 39 games. He ranked second on the team in scoring with 27 points. He also ranked second in the conference with 69 blocked shots. Following the season he was named the team's Monogram Club MVP.[7] He finished his career at Notre Dame with 16 goals and 47 assists in 143 games.[8]
On March 31, 2022, Stastney signed a two-year, entry-level contract with the Nashville Predators.[11] During his rookie season, he recorded five goals and eight assists in 56 games for the Milwaukee Admirals of the American Hockey League (AHL). He made his NHL debut for the Predators on April 1, 2023.[12] During the 2022–23 season, he recorded two points in eight games. Following the regular season, he was returned to the Admirals for the 2023 Calder Cup playoffs. During the playoffs, he recorded one goal and five assists in 16 games.[13] During game five of the division semifinals, he scored the game-winning goal with 27 seconds remaining in the game to help the Admirals advance to the Western Conference finals.[14]
On November 14, 2023, Stastney was recalled by the Nashville Predators. Prior to being recalled, he recorded one goal and three assists in ten games for the Milwaukee Admirals.[15] During the 2023–24 season he recorded two goals and two assists in 20 regular season games and was scoreless in three games during the 2024 Stanley Cup playoffs. On July 25, 2024, he signed a two-year, $1.6 million contract extension with the Predators.[16][17]