Undrafted, Kalinin played professionally in his native Russia with
Kontinental Hockey League club,
Avangard Omsk. Kalinin spent five seasons with Avangard and in the
2014–15 season, he set career highs in all categories with 12 goals, 13 assists, 25 points, 49 penalty minutes and 58 games played, while serving as the club’s captain as a 23-year-old. On May 29, 2015, Kalinin left Avangard Omsk and signed a one-year entry-level deal with the New Jersey Devils of the NHL. In the
2015–16 season, he made his NHL debut October 9, 2015 against the
Winnipeg Jets at
Prudential Center. Kalinin completed his first NHL campaign scoring eight goals and seven assists for 15 points with 33 penalty minutes in 78 games. On July 6, 2016, Kalinin opted to remain with the Devils in agreeing to a one-year contract as a restricted free agent. Kalinin would record four points in 43 games with the Devils the following season, before being placed on waivers on February 17, 2017 for the purpose of being sent to the AHL. He cleared the following day, but was traded to the
Toronto Maple Leafs in exchange for defensive prospect
Viktor Lööv. Toronto opted to trade for Kalinin instead of claim him as claiming would have put the team at the 50 contract limit heading into the March 1 trade deadline, where trading Loov allows for some deadline flexibility. He was immediately assigned to the
Toronto Marlies following the deal. After finishing the year with the Marlies, Kalinin as a free agent from the Maple Leafs, chose to return to his native Russia, signing a three-year deal with
SKA Saint Petersburg of the KHL on July 1, 2017. Approaching the
2018–19 season, Kalinin was traded by SKA to fellow powerhouse club,
HC CSKA Moscow in exchange for
Andrei Kuzmenko on August 8, 2018. Kalinin played two seasons with CSKA Moscow, before leaving as a free agent. On July 15, 2020, Kalinin agreed to a two-year contract with his fourth KHL club,
Traktor Chelyabinsk. With the
2024–25 season underway, Kalinin belatedly joined
HC Vityaz as a free agent, agreeing to a two-year contract through 2026 on 15 October 2024. ==International play==