As a freshman in 2009–10 Shore scored 5 goals and 18 assists for Denver, who won the Western Collegiate Hockey Association (WCHA) regular season title. He then led the Pioneers in scoring with 46 points and was named a WCHA Second Team All-Star in 2009–10. At the 2011 World Junior Hockey Championship, Shore appeared in six games and scored two goals. He was again named a WCHA All-Star in his junior season of 2011–12 after leading his team and finishing fourth overall in National Collegiate Athletic Association (NCAA) Division I scoring with 53 points. Shore opted to forgo his final season of college eligibility and turned professional upon the conclusion of his college season; the Panthers assigned him to their American Hockey League (AHL) affiliate, the San Antonio Rampage. Shore scored his first professional point on March 31, 2012, with an assist against the Rockford IceHogs.