Aimbetov was selected to the first Kazakh cosmonaut class in 2002, along with Mukhtar Aimakhanov, out of a pool of 2,000 candidates. From 2003 to 2009, he trained in Russia as a cosmonaut at Star City. He returned to Astana, in Kazakhstan, after failing to secure a spaceflight. He had been scheduled to fly in autumn 2009, but due to the world financial crisis, this fell through. Aimakhanov remained in Russia, becoming a Russian citizen, making Aimbetov the sole Kazakhstani cosmonaut.
In June 2015, he was selected to fly on the Soyuz TMA-18M mission in place of singer Sarah Brightman who had withdrawn in May 2015, and her backup, Satoshi Takamatsu, who had also withdrawn. The mission was projected to launch to the International Space Station on 1 September 2015. Aimbetov becomes the third Kazakh-born cosmonaut to fly since Kazakhstan's independence in 1991, and the first to fly under the Kazakh flag, and as part of KazCosmos.