2009-10: Quentin Shore played 33 games for the Colorado Thunderbirds midget minor team. He scored 13 goals with 13 assists and had 10 penalty minutes. Shore suffered a wrist injury which kept him out of the U16 Tier 1 tournament as the Thunderbirds captured Colorado's first national championship.
2010-11: Shore became the third member of his family to skate for the US National Team Development program in Ann Arbor – following in the footsteps of older brothers Drew and Nick. He skated in 52 games for the NDTP U17 team and represented the USA in three tournaments. Shore scored 4 goals with 14 assists and had 28 penalty minutes in the regular season. He had 2 assists as the USA finished first in the Four Nations Cup in Illinois. In five games at the 2011 U17 World Hockey Challenge he had 3 assists and 8 penalty minutes as the USA finished second to Canada Ontario. Shore had one assist in three games at the Vlad Dzurilla U18 tournament in Slovakia. He committed to playing college hockey at the University of Denver in 2012-13.
2011-12: Shore skated for the NDTP U18 team and was part of the gold medal USA squad at the 2012 U18 World Junior Championship. In 60 games he led the U18 team with eight game-winning goals. He finished with 17 goals and 10 assists and had 31 penalty minutes. At the U18 WJC, he scored 3 goals with 2 assists and was plus-four with 2 penalty minutes in six games as the USA won the tournament for the third straight year. Shore was ranked 80th amongst North American skaters in Central Scouting's final rankings prior to the 2012 NHL Draft.
2012-13: Shore became the third brother to play for the University of Denver, joining his older brother Nick Shore (LAK) , a junior, in the Pioneers lineup. Skating alongside fellow Colorado native Matt Tabrum for much of the season he scored 10 goals with 9 assists and had 22 penalty minutes in 39 games. Denver finished fifth in the WCHA but lost back-to-back games against eighth-seeded Colorado College in the first round. The Pioneers received an at-large bid to the NCAA tournament, falling to New Hampshire 5-2, in the Northeast Region semifinals.
Shore is a two-way forward with decent size who doesn't really have one standout area of his game. He does have a knack for scoring big goals, although he is not a highly skilled offensive player. Shore does pay attention to the defensive side of the game, but would need to bulk up some to handle the bigger bodies at the pro level.