[3] Following the 2010–11 season with the University of Denver, Shore was selected in the third round, 82nd overall by the Los Angeles Kings during the 2011 NHL Entry Draft.

As a free agent from the Jets, and with the indefinitely delayed North American season, Shore, alongside brother Drew, opted to sign a short-term contract abroad with Slovakian club, HK Dukla Trenčín of the Tipsport Liga on November 19, 2020.

Shore posted 26 points through 49 regular season games before leaving Sibir on 1 March 2022 due to the Russian invasion of Ukraine.

[18] As a free agent in the off-season, Shore returned to Switzerland after signing a one-year contract with HC Ambrì-Piotta of the NL on July 31, 2022.

[20] Following the completion of his tenure with HV71, Shore returned to North America as a free agent and was later signed to a professional tryout contract to attend the Carolina Hurricanes training camp in preparation for the 2023–24 season on August 30, 2023.

Drew is a forward for the Carolina Hurricanes of the NHL,[22] Quentin played briefly in the American Hockey League,[23] and Baker is a member of Harvard University.