Shaw, a native of Glace Bay played midget hockey in his native Nova Scotia with the Cape Breton Tradesmen.  He was chosen in the first round, 12th overall, of the 2008 QMJHL Entry Draft by the Cape Breton Screaming Eagles.

After three impressive seasons with the Screaming Eagles which saw the right winger collect 78 points, he was selected by the Panthers in the third round the 2011 NHL Entry Draft with the 76th pick.   The next season (2011-12), Shaw remained in the QMJHL with the Screaming Eagles before he was traded to the Quebec Remparts mid-way through the campaign.  In 2012-13, Shaw returned to Quebec for an overage season. He was the team’s second-leading scorer finishing with 26 goals and 42 assists in 67 games, and was a team-best +30 with 37 penalty minutes.

In April, 2013, Shaw was signed by the Florida Panthers to a three-year entry-level contract. He was assigned to begin his professional career with AHL affiliate, the San Antonio Rampage.   

During the 2015-16 season, Shaw received his first NHL recall after beginning the year with the Panther’s new AHL affiliate, the Portland Pirates. He made his NHL debut with the Panthers on October 30, 2015. He skated in 53 regular season games and three playoff contests for Florida. Shaw scored 5 goals with 2 assists and was -7 with 13 penalty minutes, averaging 12:14 minutes of ice time during the regular season.