Greer, a second-round pick (No. 39) of the Colorado Avalanche in the 2015 NHL Draft, eventually found his footing in the League when he signed a two-year contract with the Florida Panthers on July 1, 2024. He scored his first Stanley Cup Playoff goal during Florida's 6-1 win against the Toronto Maple Leafs in Game 5 of the Eastern Conference Second Round and his second-period goal was the game-winner in the opener of the Eastern Conference Final, a 5-2 victory against the Carolina Hurricanes that continued the road to the Panthers' second consecutive -- and Greer's first -- Stanley Cup championship.

Greer played 278 American Hockey League games for San Antonio (2016-17 to 2017-18), Colorado (2018-19 to 2019-20), Bridgeport (2020-21), Binghamton (2020-21) and Utica (2021-22). He was named to the 2017 AHL All-Star Game and was awarded the Yanick Dupre Memorial Award for his community efforts at the conclusion of the 2016-17 season. He was alternate captain for the 2015-16 Quebec Major Junior Hockey League champion Rouyn-Noranda and played two seasons at Boston University (2014-16), where as a freshman he helped the Terriers win the Hockey East regular season title and conference championship.