As a result of his major junior ice hockey play, Pelech was selected by the Islanders in the third round, 65th overall, of the 2012 NHL Entry Draft.

Pelech spent the majority of his first two seasons with the Islanders organization with their American Hockey League affiliate, the Bridgeport Sound Tigers, before making the jump to the NHL level.

He was soon considered an elite stay-at-home defenceman and was subsequently selected to represent the Islanders at the 2022 National Hockey League All-Star Game.

[4] Pelech played minor ice hockey with the Toronto Marlboros under Connor Brown's father, whom he later listed as a huge influence on his career.

[3] Pelech helped the Marlboros qualify for the 2010 Ontario Hockey League (OHL) Cup by tallying six goals and 28 assists in 69 games.

[10] Prior to his sophomore season, Pelech was invited to attend Canada's Mens Summer Under-18 Team selection camp leading up to the 2011 Ivan Hlinka Memorial Tournament.

[11] He subsequently helped Team Canada win their fourth straight gold medal at the tournament before returning to North America.

[13] Following the game, Pelech earned a midterm ranking of 54th from the NHL Central Scouting Bureau[14] and was selected to represent Team Canada at the 2012 IIHF World U18 Championships.

[22] Following the Islanders' 2014 training camp, Pelech was loaned to their American Hockey League (AHL) affiliate, the Bridgeport Sound Tigers, to start the 2014–15 season.

[30] During this recall, Pelech tallied his first career NHL goal on November 23 in the first period to help the Islanders win 3–2 over the Ducks.

[34] He finished the season with three goals and seven assists in 44 games with the Islanders and earned praise from the teams' general manager Garth Snow as being "an important piece of our defensive core."

[36] Early in the season, Pelech impressed coach Doug Weight enough that he was given a chance on the Islanders second power-play unit alongside Josh Bailey, Mathew Barzal, Andrew Ladd, and Brock Nelson.

[38] Upon returning, Pelech experienced an uptake in offensive output and set career highs in both assists and points by December.

[2] During the 2018 offseason, Calvin de Haan left the Islanders for the Carolina Hurricanes and Pelech was expected to replace him in the lineup.

[46] In the first round of the 2019 Stanley Cup playoffs, Pelech tallied two assists through an average 86:21 minute of ice time as the Islanders swept the Penguins.

[49] His season would be short-lived however as he suffered an injury to his Achilles tendon during the pregame warmup prior to a January game against the New Jersey Devils.

[61] On January 13, 2022, it was announced that Pelech would make his first NHL All-Star Game appearance on February 6, 2022, in Las Vegas, Nevada.

[12] The following year, he was again chosen to represent Team Canada on the international stage during the 2012 IIHF World U18 Championships where he helped them win a bronze medal.