Since turning professional in the 2009–10 season, Smith, while within the Predators organization, was shuffled between the Milwaukee Admirals of the 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 8 weeks due to this injury, Smith was recalled from his loan with Iowa Wild to provide Providence cover. In Subban's absence, Smith was a stand out 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. At the conclusion of 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 injury to starting goaltender Semyon Varlamov, and backed upCalvin 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 teams 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. In the following 2017–18 season, Smith was unable to add to his NHL experience, assigned to AHL affiliate, the 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 KHL.
