Gostisbehere's background would seem to suggest he was unlikely to become an NHL player. The son of a former professional jai alai player from France, he was born in Pembroke Pines, Florida, on April 20, 1993, six months before his hometown Florida Panthers began play in the League.

From an early age, the player his teammates call "Ghost" was always around a hockey rink, tagging along when his older sister had figure skating lessons and joining fans in throwing plastic rats onto the ice after Panthers victories.

Before long, Gostisbehere decided to try the ice out for himself, learning how to skate at the Incredible Ice facility where the Panthers practiced in Coral Springs and joining the Junior Panthers youth hockey program.

Gostisbehere was selected by the Philadelphia Flyers in the third round (No. 78) in the 2012 NHL Draft after the first of his three seasons at Union College in Schenectady, New York. He is the first player born and raised in South Florida to make it to the NHL.

He's quite a good one, too. In 2015-16 he finished second to Artemi Panarin in balloting for the Calder Trophy, awarded to the NHL's top rookie, after he led Flyers defensemen and ranked 17th in the NHL at the position with 46 points (17 goals). He also was selected to the 2016 NHL All-Rookie Team.

Eighteen of his points in 2015-16 came during a 15-game point streak from Jan. 19-Feb. 20, the longest ever by a rookie defenseman in the NHL. Gostisbehere was five games short of Paul Stastny's record for the longest point streak by a rookie in the modern era, set in 2007. It was the longest streak by an NHL defenseman since Chris Chelios' 15-game streak in 1995.

The last point in Gostisbehere's streak came on an overtime goal in the Flyers' 5-4 win against the Toronto Maple Leafs. In that game he also became the first rookie in NHL history to have four overtime goals in a season.

He scored 65 points (13 goals, 52 assists) in 78 games in 2017-18 and finished 10th in voting for the Norris Trophy, given to the top defenseman in the NHL.

Gostisbehere was traded to the Arizona Coyotes on July 22, 2021, for two picks in the 2022 NHL Draft. In Gostisbehere's first season with the Coyotes, he played 82 games for the first time in his NHL career while scoring 51 points (14 goals, 37 assists) while averaging 22:11 of ice time per game. He had 31 points (10 goals, 21 assists) through 52 games of 2022-23 before he was traded to the Carolina Hurricanes on March 1 for a third-round pick in the 2026 NHL Draft.

Gostisbehere signed a one-year, $4.125 million contract with the Detroit Red Wings on July 1, 2023. He signed a three-year, $9.6 million contract with the Carolina Hurricanes on July 1, 2024.