Postma has played major junior in the WHL for the Swift Current Broncos and Calgary Hitmen. After a 24-point season in 2006–07, he was drafted in the 7th round, 205th overall, by the Atlanta Thrashers in the 2007 NHL Entry Draft. The next season, he was traded to the Calgary Hitmen, where he recorded 14 goals and 42 points. In 2008–09, Postma emerged with a 23-goal, 84-point campaign, first among league defencemen, setting team records for single-season goals and points by a defenceman. in 2013. He earned WHL East First Team All-Star honours, along with teammates Brandon Kozun and Brett Sonne and a nomination for the Bill Hunter Memorial Trophy as the league's top defenceman, opposite Jonathon Blum of the Vancouver Giants. With a league-high +67 plus-minus rating, he won the WHL Plus-Minus Award. During the second round of the subsequent 2009 playoffs, Postma was signed to a three-year, entry-level contract by the Thrashers. He finished the 2009 playoffs with 13 points in 18 games, as the Hitmen were defeated in the finals by the Kelowna Rockets. While playing for the Winnipeg Jets, Postma scored his first NHL goal on February 1, 2013, against Anders Lindbäck of the Tampa Bay Lightning. In 2013–14, Postma missed most of the season due to injury, including a blood clot that had him sidelined for 47 games. Postma played a total of 42 games for the Jets during the 2014–15 season, but was sidelined in March, due to a lower-body injury. On July 10, 2015, Postma signed a two-year, $1,775,000 contract extension with the Jets. After spending his first eight professional seasons with the Thrashers/Jets franchise, Postma left as a free agent in agreeing to terms with the Boston Bruins on a one-year, $775,000 contract on July 1, 2017. He split the 2017–18 season between Boston and AHL affiliate, the Providence Bruins. As a free agent from the Bruins, Postma opted to halt his North American career, agreeing to a one-year contract with Russian champions, Ak Bars Kazan of the Kontinental Hockey League, on August 15, 2018. In the 2018–19 season, Postma regained his scoring touch in the KHL, posting 8 goals and 28 points through 57 regular season games. On May 1, 2019, Postma left Ak Bars as a free agent to sign a one-year contract with Russian outfit, Metallurg Magnitogorsk. He made just 10 appearances with Magnitogorsk to open the 2019–20 season before opting to leave the KHL on October 6, 2019. Moving to continue his career in Switzerland, after a successful tryout, Postma joined HC Lugano of the National League on a one-year deal on November 6, 2019.
