The Islanders selected Pelech in the third round (65th overall) of the 2012 National Hockey League Draft. He has 75 points (16 goals, 59 assists) in 303 career NHL games along with 12 points (two goals, 10 assists) in 48 career playoff games.

He began his professional career in 2014-15 with the Islanders American Hockey League affiliate in Bridgeport, scoring 23 points (three goals, 20 assists) in 105 games over three seasons. Pelech played junior hockey with the Erie Otters of the Ontario Hockey League, totaling 127 points (20 goals, 107 assists) with 223 penalty minutes in 228 games.

On the international stage, Pelech represented Canada at the 2014 World Junior Championships and the 2012 World Under-18 Junior Championships, winning bronze in 2012. He also won gold with Team Canada-Ontario at the 2011 Under-17 World Hockey Challenge.