Shore played three seasons at the University of Maine after being selected by the Dallas Stars in the second round (No. 61) of the 2012 NHL Draft.

Shore was named to Hockey East's First Team after his sophomore season in 2013-14, when he scored 43 points (14 goals, 29 assists) in 35 games. He left school after his junior season and signed a three-year contract with the Stars on March 10, 2015.

Shore made his NHL debut against the Boston Bruins on Nov. 12, 2015 but played three games for the Stars that season. He scored his first NHL goal against the Colorado Avalanche on Oct. 15, 2016.

He played all 82 games for the Stars in 2016-17 and set NHL career highs in goals (13) and points (33). He did not miss a game the following season and finished with 32 points (11 goals, 21 assists).

Shore was traded by the Stars to the Anaheim Ducks for forward Andrew Cogliano on Jan. 14, 2019. In 34 games with Anaheim, he had five goals and seven assists.

He was traded again midway through the following season, this time to the Blue Jackets for forward Sonny Milano on Feb. 24, 2020.

NOTES & TRANSACTIONS

• Hockey East First All-Star Team (2014)
• NCAA East Second All-American Team (2014)
• Hockey East Second All-Star Team (2015)
• Traded to Anaheim by Dallas for Andrew Cogliano, January 14, 2019.
• Traded to Columbus by Anaheim for Sonny Milano, February 24, 2020.