Stillman is the second generation of his family to play in the NHL. His father, Cory Stillman, was a forward who played three of his 16 seasons with the Florida Panthers before retiring in 2011.

Riley, a defenseman, was selected by the Panthers in the fourth round (No. 114) of the 2016 NHL Draft. After being selected, he played two more seasons of junior hockey with Oshawa and Hamilton in the Ontario Hockey League before signing a three-year, entry-level contract with Florida on March 4, 2018.

Stillman played his first professional season with Springfield of the American Hockey League, where he had 17 points (four goals, 13 assists) in 59 games, but he did make his NHL debut in a 4-3 shootout loss to the Arizona Coyotes on Feb. 26, 2019.

The Panthers sent Stillman back to Springfield for the start of the 2019-20 season, but he was recalled for good on Dec. 27, 2019. He was credited with his first NHL point, an assist, in a 6-3 win against the Ottawa Senators on Jan. 2, 2020, and finished the season with five assists in 34 games.

Stillman was traded to the Chicago Blackhawks on Oct. 7, 2022. He had five assists in 32 games until he was traded to the Buffalo Sabres on Feb. 27, 2023.

Stillman signed a one-year contract with the Carolina Hurricanes on July 1, 2024.