After turning professional with the Predators organization in the 2009–10 season, Smith was shuffled between the
Milwaukee Admirals of the
American Hockey League (AHL) and the
Cincinnati Cyclones of the
ECHL. On July 5, 2013, Smith signed a one-year contract as a free agent with the
Columbus Blue Jackets. After attending the Blue Jackets training camp, he was assigned to AHL affiliate, the
Springfield Falcons. . On July 2, 2014, Smith signed a one-year,
two-way contract with the Boston Bruins. Smith was sent down to
Providence Bruins to be a call-up along with
Malcolm Subban for the majority of the season. On July 1, 2015, the Boston Bruins re-signed Smith to a one-year, two-way contract. With Smith unable to earn the backup role and with the Bruins suffering a surplus of goaltenders in their system, he was assigned on loan to AHL affiliate club of the
Minnesota Wild, the
Iowa Wild, for the duration of the
2015–16 season on October 6, 2015. On February 6, 2016, Providence's
Malcolm Subban was hospitalized after taking a puck to the throat. With Subban ruled out for eight weeks due to this injury, Smith was recalled from his loan with the Iowa Wild to provide Providence with cover. In Subban's absence, Smith was a standout for Providence, posting 13 wins in 20 games and earning his first recall to the NHL, on an emergency basis, on April 9, 2016. He was returned to the AHL for the post-season without featuring for the Bruins. After the season, Smith left the Bruins organization as a free agent. On July 1, 2016, he signed a one-year, two-way contract to join the
Colorado Avalanche. Smith began the
2016–17 season in the AHL with affiliate, the
San Antonio Rampage. He was injured in his third game with the Rampage and missed two months of action before returning to post his first win with the Rampage in a 4–2 victory over the
Tucson Roadrunners on December 17, 2016. On December 27, Smith was recalled by the Avalanche after an injury to starting goaltender
Semyon Varlamov and backed up
Calvin Pickard for five games before he was returned to the Rampage on January 5, 2017. With Varlamov suffering a season-ending injury, Smith was recalled on a second occasion on February 9, 2017. He made his NHL debut with the Avalanche, making 37 saves in a 3–2 defeat to the
New Jersey Devils on February 14, 2017. In his third start with the Avalanche he received his first NHL win, making 34 saves in the team's 5–3 win over the
Buffalo Sabres on February 25, 2017. As a free agent in the off-season, Smith left the Avalanche to sign a one-year, two-way contract with the
Carolina Hurricanes on July 1, 2017. For the following
2017–18 season, Smith was unable to add to his NHL experience, assigned to the AHL affiliate
Charlotte Checkers for the duration of the campaign. In 30 games, Smith collected 13 wins and posted a goals against average of 2.71. At the completion of his contract with the Hurricanes, Smith became a free agent and agreed to sign a one-year AHL contract with the
Bridgeport Sound Tigers on July 9, 2018. In the following
2018–19 season, Smith had collected 16 wins through 32 games for the Sound Tigers before he was signed to a two-way contract by the
New York Islanders for the remainder of the year on February 24, 2019. In adding depth to the goaltending ranks of the playoff-bound Islanders, Smith would continue to play with their AHL affiliate. On June 10, 2019, Smith as an impending free agent, signed his first contract abroad, agreeing to a two-year contract with Chinese outfit
Kunlun Red Star of the
Kontinental Hockey League (KHL). Smith played six seasons with the team, becoming a
KHL All-Star twice in 2024 and 2025. Amid the team's relocation to become the
Shanghai Dragons, though, Smith's contract was terminated, making him a free agent. ==International play==