Pesce attended Irvington High School in New York, and played varsity on a joint Irvington-Sleepy Hollow hockey team, graduating in June 2012.

Having played 109 games with the Wildcats, Pesce opted to forgo his final year of eligibility signing a three-year, entry-level contract with the Carolina Hurricanes on March 27, 2015.

[2] He was signed to an amateur try-out contract with the Hurricanes' American Hockey League (AHL) affiliate, the Charlotte Checkers, and made his professional debut on April 2, against the Oklahoma City Barons.

[3] He was returned to the Checkers, however during his second recall to the Hurricanes made his NHL debut in a 5–2 loss against the San Jose Sharks on October 24.

On February 22, 2020, Pesce suffered a right shoulder injury against the Toronto Maple Leafs, and was later ruled out for the remainder of the campaign undergoing season-ending surgery.