Prince was selected in the second round, 61st overall, in the 2011 NHL Draft by the Ottawa Senators. The pick Ottawa used to select Prince was obtained from the Boston Bruins in the Chris Kelly trade. Playing with the Binghamton Senators he scored his first professional goal against the Rochester Americans on November 17, 2012. He deflected a shot from teammate Tyler Eckford past Americans' goaltender David Leggio. After recording 18 goals and 38 points in 47 games with the Binghamton Senators of the American Hockey League Prince made his NHL debut with the Senators on February 16, 2015 vs the Carolina Hurricanes. Prince registered an assist in the game. He played one additional game with Ottawa and was then returned to Binghamton. Prince would go on to lead the Binghamton Senators in scoring tallying 28 Goals, 37 Assists for 65 Points while being selected to the season ending AHL All-Star Team. Prince started the 2015–16 season with the Ottawa Senators, scoring his first NHL goal on November 25, 2015 against the Colorado Avalanche in Colorado. He finished the game with two goals and one assist and was selected as the game's first star. Although being among the team leaders in points production per 60 minutes played he was often inexplicably scratched by Senators coach Dave Cameron. To the angst of many Senators fans, Prince was traded to the New York Islanders on February 29, 2016, along with a seventh round pick, in exchange for a third round pick in the 2016 NHL draft. Senators GM Bryan Murray stated in a press conference that Prince "wasn't playing much here, he deserved to play". Six weeks after trading Prince the Ottawa Senators fired Dave Cameron and the entire coaching staff. Prince played a regular shift for the Islanders for the remainder of the season scoring 3 goals and 2 assists in 20 games helping New York qualify for the Stanley Cup Playoffs. Prince scored his first NHL playoff goal on April 17, 2016 in game three of the first round vs the Florida Panthers. The Islanders eliminated the Panthers in six games winning their first playoff series in 23 years. In game one of the second round vs the Tampa Bay Lightning, Prince scored two goals in the first period leading the Islanders to a 5-3 victory in Tampa on April 27, 2016. Prince was named the game's first star and became the youngest Islander in 28 years to score two goals in a playoff game and the first Islander in 34 years to score a pair of first period goals in a playoff game. The Lightning eliminated the Islanders in five games with Prince finishing tied for second in team playoff goals with three. On July 1, 2016, Prince signed a two-year contract extension with the Islanders valued at $1.7 million. As an impending restricted free agent following the 2017–18 season, Prince was not tendered a qualifying offer by the Islanders resulting in his status as an unrestricted free agent on June 25, 2018. On August 4, 2018, Prince opted to embark on a European career, after signing a two-year contract worth CHF 1.2 million with Swiss club, HC Davos of the National League. However, on November 16, Prince terminated his contract with Davos after 16 games, stating that he intended to return to the NHL. Unable to find a contract offer from the NHL, Prince subsequently signed a contract in the KHL with HC Sibir Novosibirsk, who acquired his rights from HC Vityaz on November 21, 2018. The following season, he signed with Dinamo Minsk.
