Kvitelashvili won the bronze medal at the 2015 CS Mordovian Ornament in Saransk, Russia. He finished twelfth at his sole GP event, the 2015 Cup of China. In December 2015, he placed fifth in his final international event for Russia, the CS Golden Spin of Zagreb, and twelfth at the Russian Championships. In May 2016, he submitted a request to Russian skating officials to be released to compete for Georgia.