He played two seasons in the NCAA with the University of New Hampshire, in 2005–07. There, he was an All Hockey East First team selection, an NCAA East Second Team All-American, and was named to the New England All-Star team.[4][7] He had 63 points in 78 games over two seasons.[8]
During the 2007–08 season, Trevor split time between the Utah Grizzlies and the Bridgeport Sound Tigers, playing 53 games in Bridgeport and 22 in Utah. He was picked to represent Utah at the ECHL All-Star game, but could not play as he was recalled to Bridgeport.[7] He was named the Rbk Edge/AHL Rookie of the Month for February 2008 after scoring 15 points in 13 games.[4][7]
Smith had a breakout year during the 2008–09 season for the Sound Tigers playing on the first line between Kurtis McLean and Mike Iggulden, scoring 30 goals and notching 32 assists in 76 games. Trevor made his NHL debut with the Islanders later that season, wearing number 77 and scoring one goal in seven games.
On July 2, 2010, Smith signed as a free agent to a one-year contract with the Anaheim Ducks.[9]
In 2011–12, he played in the AHL All-Star Game, had an AHL Best Plus/Minus (+34), played for the AHL Calder Cup Champion, and had the AHL Most Points Playoffs (16).[6]
On July 1, 2012, Smith was signed to a one-year, two-way contract with the Pittsburgh Penguins.[10] Due to the NHL lockout, Smith was directly assigned to the Penguins AHL affiliate, the Wilkes-Barre/Scranton Penguins for the majority of the 2012–13 season. He was briefly recalled by the Penguins and played a solitary game against the New York Islanders on March 22, 2013.
During the summer of 2013 he was recruited to play for Team Canada in the 2013 Maccabiah Games in Israel, but was recovering from an upper-body injury sustained during the AHL playoffs and turned down the request; his father was assistant coach to the team, and it won a gold medal.[5][11] He said: "I would have been upset if Canada had lost because I had not gone".[5]
On October 4, 2013, Smith was named as team captain of the Toronto Marlies – the Maple Leafs' AHL affiliate, becoming the 5th Captain in team history.[5][14] On October 8 he debuted for the Leafs, becoming the 900th player in franchise history.[15]
On July 2, 2015, Smith as a free agent signed his first contract abroad, agreeing to a two-year contract with Swiss club, SC Bern of the National League A (NLA).[16] He won the 2016 Swiss championship with Bern, but missed large parts of the 2015-16 season after undergoing elbow surgery. He returned to game action in February 2016.[17] During his Bern stint, Smith made 18 NLA appearances producing three goals and two assists and played in four contests of the Champions Hockey League, scoring one goal and two assists. He left after a single season at SCB.
On July 2, 2016, he inked a two-year, two-way contract with the Nashville Predators of the National Hockey League (NHL).[18] Smith made his debut with the Predators in a solitary game during the 2016–17 season, spending the duration of his contract with Nashville's AHL affiliate, the Milwaukee Admirals.
As a free agent from the Predators, Smith agreed to a one-year AHL contract to add a veteran presence to the San Antonio Rampage on July 30, 2018.[19]
