Brickley can play all three forward positions. He had 12 points (four goals, eight assists) in 44 games in 2017-18, his second NHL season.
The Florida Panthers selected Brickley in the second round (No. 50) of the 2010 NHL Draft. He played four seasons at the University of Vermont, scoring the game-winning goal against Massachusetts in the first round of the 2014 Hockey East Tournament and helping Vermont qualify for the NCAA Tournament. He also played for the United States at the 2012 IIHF World Junior Championship.