Kuat scored his first goal for Kazakhstan on 10 October 2015 in a 2–1 defeat against the Netherlands in a UEFA Euro 2016 qualifier.

[1] On 30 December 2019, FC Kairat confirmed Kuat's departure from the club at the end of his contract.

[2] On 1 January 2020, Russian Premier League club FC Orenburg announced the signing of Kuat.

[6] On 16 March 2021, FC Astana announced that they had re-signed Kuat after he'd previously played for the club between 2010 and 2014.

A dozen Turkish fans presented him with gifts and a bouquet of flowers, and thanked him personally at half-time during Kairat's game against Atyrau on 17 October.