Shaw played midget hockey within his native Nova Scotia with the Cape Breton Tradesmen before joining the major junior ranks with the Cape Breton Screaming Eagles of the Quebec Major Junior Hockey League (QMJHL), after he was selected 12th overall in the 2008 QMJHL Entry Draft.

[2] Shaw was assigned to begin his professional career with the Panthers' American Hockey League (AHL) affiliate, the San Antonio Rampage, in the 2013–14 season.

[3] In the 2015–16 season, after five games with new AHL affiliate, the Portland Pirates, Shaw received his first NHL recall to the Panthers on October 29, 2015.

He was re-assigned to Portland in March 2016 before being recalled for the 2016 Stanley Cup Playoffs[3] and featured in three post-season games in the Panthers' first-round defeat.

[6] In the 2016–17 season, Shaw was unable to retain his role with the Panthers and was reassigned to inaugural AHL affiliate, the Springfield Thunderbirds.

He scored four goals in 13 games with the Thunderbirds before he was traded by the Panthers to the Anaheim Ducks in exchange for Michael Sgarbossa on November 16, 2016.

[8] Shaw was inserted into the Canadiens lineup and played out the remainder of the season, appearing in 30 games for 2 goals and 6 points.

[10] Un-signed over the summer, Shaw accepted an invitation and attended the Calgary Flames 2018 training camp.