[1] On 26 August 2017, Suter scored a Champions Hockey League (CHL) record of four goals with the Lions in an 11–1 win against French team, Rapaces de Gap.

[4][5] Prior to the start of the 2018–19 season, the ZSC Lions announced that Suter had been included in the training camp roster for the New York Islanders.

[7] On 13 July 2020, Suter announced he was leaving the NL and the ZSC Lions, using his exit-clause in his contract in order to pursue his career in North America and the NHL.

Suter scored his first NHL goal, as well as his first career hat trick, on 24 January against Jonathan Bernier of the Detroit Red Wings.

[13] He became the second player in franchise history to score each of his first three career NHL goals in the same game, joining Bill Kendall on 17 December 1933.

[17] Suter was added to the Swiss national team at the senior level in preparation for the 2017 IIHF World Championship.