Selected by the Chicago Blackhawks in the fourth round (No. 121) in the 2013 NHL Draft, Motte is a pesky, undersized presence (5-foot-10, 192 pounds) who has been compared to Andrew Shaw.

With the University of Michigan in 2015-16, Motte finished in the top 10 in the Hobey Baker Award voting after scoring 32 goals and 56 points in 38 games and leading the NCAA with 70 blocked shots. He was selected to the Big Ten First All-Star Team and the NCAA West First All-American Team. He turned pro at the end of the season and scored five points in five games for Rockford of the American Hockey League.

Like Blackhawks forward Patrick Kane, Motte played youth hockey for Detroit Honeybaked. He played two seasons (2011-13) with the USA Hockey National Team Development Program, competing in the United States Hockey League and against college and international teams. He tied for third on the Under-17 team in 2011-12 with 41 points and finished third with 25 goals. The next season he tied for the team lead with 26 goals and had 44 points in 63 games.

Motte finished second with the United States at the 2013 IIHF World Under-18 Championship, where he had a team-high five goals and seven points in seven games.

At Michigan, he scored nine goals and 18 points and was plus-9 as a freshman in 2013-14. He was third on the Wolverines with 22 assists the following season and led them with 43 blocked shots. He had four assists, the most by a Michigan player in six seasons, in an 8-3 win against rival Ohio State.

Motte represented the United States at the 2015 IIHF World Junior Championship and had one assist in five games. He scored one goal and three points in 10 games for the U.S. at the 2016 World Championship.

He split the 2016-17 season between the Blackhawks and Rockford, scoring four goals and seven points in 33 games for Chicago. Motte was then traded twice in less than a year; first to the Columbus Blue Jackets on June 23, 2017, and then to the Vancouver Canucks on Feb. 26, 2018.

Motte had 15 points (seven goals, eight assists) in 58 regular-season games for the Canucks and New York Rangers in 2021-22. He did not have a point in nine games with the Rangers after being traded March 21, but scored two goals in 15 Stanley Cup Playoff games to help New York reach the Eastern Conference Final. He agreed to a one-year, $1.35 million contract with the Ottawa Senators on Sept. 14, 2022.

Motte returned to the Rangers when he was acquired in a trade with the Senators on Feb. 19, 2023, for forward Julien Gauthier and a conditional seventh-round pick in the 2023 NHL Draft. He signed a one-year, $800,000 contract with the Tampa Bay Lightning on Sept. 9, 2023.

Motte signed a one-year, $800,000 million contract with the Detroit Red Wings on July 2, 2024.