Beck was drafted by the Nashville Predators in the third round, 70th overall, in the 2009 NHL Entry Draft. He was signed to a three-year entry level contract with the Predators on August 25, 2010. During the lock-out shortened 2012–13 season, Beck received his first recall from the Milwaukee Admirals and made his NHL debut with the Predators in a 4–3 defeat to the Columbus Blue Jackets on March 19, 2013. In his third game with Nashville, also against the Blue Jackets, Beck scored his first NHL goal in a multi-point game victory on March 23, 2013. Following the 2014–15 NHL season Beck became a restricted free agent under the NHL Collective Bargaining Agreement. The Nashville Predators made him a qualifying offer to retain his NHL rights and, on July 5, 2015, Beck filed for Salary Arbitration. On July 12, 2015, Beck's rights were traded to the Toronto Maple Leafs in exchange for forwardJamie Devane. He would sign a one year contract with the club the following day. On the eve of the Maple Leafs training camp, on September 17, 2015, Beck was again traded, along with a group of prospects, to the New York Islanders in exchange for Michael Grabner. Beck was later assigned by the Islanders to begin the 2015–16 season in the AHL with affiliate, the Bridgeport Sound Tigers. After a month in Bridgeport, Beck was recalled by the Islanders on October 31 made later made his debut with the club in a 2–1 defeat to the Boston Bruins on November 8, 2015. Beck remained on the Islanders roster for a month appearing in only 1 further game before he was re-assigned to the Sound Tigers on November 26, 2015. Beck added to the Bridgeport offence with 33 points in 46 games before he was dealt by the Islanders, for the third time within the year, to the Colorado Avalanche in exchange for Marc-André Cliche on February 29, 2016. He was directly assigned to remain in the AHL with the San Antonio Rampage. At the conclusion of the season as a restricted free agent, Beck was not tendered a qualifying offer to remain with the Avalanche. As a free agent, Beck agreed to a one-year, two-way contract with the Edmonton Oilers on July 3, 2016. Assigned to affiliate, the Bakersfield Condors to begin the 2016–17 season, Beck led the team and was amongst the AHL scoring leaders before he was recalled to the Oilers. Beck appeared in 3 scoreless games with the Oilers before he was returned to the Condors. He amassed 50 points in just 40 games before he was dealt at the NHL trade deadline by the Oilers to the New York Rangers in exchange for Justin Fontaine on March 1, 2017. Beck continued scoring at a point-per-game pace with affiliate, the Hartford Wolf Pack, and featured in 2 regular season games with the Rangers to end the season. With 76 points in 56 games, Beck was selected to the AHL's First All-Star Team. As an impending free agent, on June 13, 2017, Beck signed a one-year deal with Russian club, Avtomobilist Yekaterinburg, of the Kontinental Hockey League. During the 2018–19 season, while in his second season with Kunlun Red Star, Beck continued his scoring pace with the club in notching 9 goals and 22 points through 39 games before he was traded to Avangard Omsk in exchange for the rights to Axel Holmström on December 27, 2018. On June 4, 2020, during the off-season, Beck was traded by Omsk to Metallurg Magnitogorsk in exchange for Ilya Kablukov and Alexei Bereglazov.
