At season's end, Burmistrov became a restricted free agent and subsequently signed a two-year contract with Ak Bars Kazan of the Kontinental Hockey League (KHL).

[4] In a disappointing start to the 2016–17 season in which he scored only 2 points in 23 games with Winnipeg, Burmistrov was placed on waivers on 1 January 2017 and was subsequently claimed by the Arizona Coyotes.

On 24 December 2017, his agent, Dan Milstein, released a statement on Twitter that stated Burmistrov had "retired from the NHL" and that an announcement on his future was forthcoming.

[10] During the 2018–19 season, Burmistrov struggled to gain his offensive touch, registering just 5 points in 27 games for the defending champions before he was traded to Salavat Yulaev Ufa in exchange for three prospects on 1 December 2018.

He added a goal and assist in Salavat's opening round victory over Avangard Omsk before the remainder of playoffs were cancelled due to the COVID-19 pandemic.

[citation needed] As a free agent, Burmistrov returned home to Ak Bars Kazan, agreeing to a one-year contract for his fourth stint with the club on 5 June 2020.