2009-10: Gilmour skated for the South Shore Kings and Boston Advantage U16 teams. He competed in the Beantown Classic's pre-draft division in March and committed to playing college hockey at Quinnipiac in 2013-14.
2010-11: Gilmour played for the Noble and Greenough School in Massachusetts in the New England Prep School League. Transferring to the school as a sophomore, he scored 11 goals with 16 assists and had 8 penalty minutes in 27 games for the Bulldogs. Noble and Greenough finished with a 17-10 record, losing to eventual prep champion Milton Academy in triple overtime in the New England prep quarterfinals.
2011-12: Gilmour was the leading scorer for Noble and Greenough as the Bulldogs finished 23-5-1 and reached the New England prep championship game. In 28 games he scored 26 goals with 30 assists. Noble and Greenough lost to Lawrence Academy, 3-2, in the championship game. Gilmour de-committed from attending Quinnipiac and committed to playing college hockey at Boston College. Ranked 101st amongst North American skaters in Central Scouting's final rankings, he was selected by Minnesota in the fourth round (98th overall) of the 2012 NHL Draft.