Kalinin became an unrestricted free agent July 1, 2008 and two days later signed a one-year contract with the New York Rangers.

On March 4, 2009, Kalinin was traded to the Phoenix Coyotes along with Petr Průcha and Nigel Dawes for Derek Morris.

[1] On July 21, 2009, Kalinin signed a two-year contract with the Salavat Yulaev Ufa of the Kontinental Hockey League (KHL).

[2] Kalinin was named a member of Russia's hockey team for the 2010 Winter Olympics in Vancouver, British Columbia.

On May 6, 2019, Kalinin as a free agent continued his career by returning to hometown club, Traktor Chelyabinsk, on a one-year contract.