Biega was selected by the Buffalo Sabres in the 5th round (147th overall) of the 2006 NHL Entry Draft and played the majority of his career with the Vancouver Canucks.

[5] He attended his first Sabres training camp, but was cut and sent to the team's American Hockey League (AHL) affiliate, the Portland Pirates.

[4] Biega spent the entire 2011–12 season with the Rochester Americans, the new AHL affiliate of the Buffalo Sabres.

[9] He was assigned to AHL affiliate, the Utica Comets for their inaugural season in 2013–14, appearing in a career-high 73 games for 22 points from the blueline.

[16] At the start of the 2016–17 NHL season, Biega made the Canucks out of training camp, but only appeared in one game as a forward before being sent down to the Comets for a conditioning stint in November.

[17] Biega made the Canucks out of camp again at the start of the 2018–19 NHL season, but was sent down to Utica on October 18 not having played a game.

[18] He was recalled on October 25[19] and scored his first goal of the season and second overall for the Canucks in an overtime loss to the Chicago Blackhawks on February 7, 2019.

[26] During the pandemic-shortened 2020–21 season, Biega was placed on waivers for the purpose of transferring him to the Red Wings' taxi squad.

[28] On July 28, 2021, having left the Red Wings as a free agent, Biega was signed to a one-year, two-way contract with the Toronto Maple Leafs.

[35] While with the Vancouver Canucks, Biega became involved with the National Hockey League Players Association's Core Development Program, which helps former NHL players transition from their hockey careers post retirement, helping to develop the program.