Shaw, a native of Glace Bay, Nova Scotia, was taken in the third round (No. 75) of the 2011 NHL Draft by the Florida Panthers after putting up 46 points (26 goals, 20 assists) in his second season for Cape Breton of the Quebec Major Junior Hockey League. He split 2011-12 between Cape Breton and Quebec, then had his best offensive season in the QMJHL for Quebec in 2012-13, finishing with 68 points (26 goals, 42 assists).

The Panthers signed him to a three-year, entry-level contract on April 22, 2013, and he began his pro career in 2013-14 with San Antonio of the American Hockey League. Shaw earned his first callup to the NHL on Oct. 29, 2015, and played his first game one night later against the Boston Bruins. He scored his first NHL goal on Dec. 8, 2017, against the Ottawa Senators and finished the season with five goals and seven points in 53 games.

But after failing to make the Panthers in training camp in the fall of 2016, Shaw was returned to the minors before being traded to the Anaheim Ducks on Nov. 16, 2016. He played the rest of the season for the Ducks, finishing with 10 points (three goals, seven assists) in 55 games.

Shaw spent the first half of the 2017-18 season with the Ducks, but after Anaheim picked up forward J.T. Brown off waivers, the Ducks waived him and he was claimed by the Montreal Canadiens on Jan. 15, 2018. He scored his first goal for the Canadiens against the Ducks on Feb. 3, 2018.

However, the Canadiens did not re-sign him, and he signed with the Winnipeg Jets organization on Nov. 11, 2018. After spending 2018-19 and starting 2019-20 in the AHL, was recalled by the Jets and spent most of the season with Winnipeg.

NOTES & TRANSACTIONS

• Traded to Anaheim by Florida for Michael Sgarbossa, November 16, 2016.
• Claimed on waivers by Montreal from Anaheim, January 15, 2018.
• Signed as a free agent by Winnipeg, November 11, 2018.
• Signed as a free agent by Ottawa, October 9, 2020.