[1] Representing Georgia, Kajaia participated in the 2013 Summer Universiade and he won the bronze medal in the 96 kg event.

[2] He was part of the Georgian Wrestling Team at the 2015 European Games but lost to Italian Daigoro Timoncini at the 1/8 finals.

He entered the 2017 European Wrestling Championships in Novi Sad, Serbia but defeated by the Olympic champion Artur Aleksanyan in the second round.

[5] At the 2018 Mediterranean Games in Tarragona, Spain, he lost to the eventual champion, Frenchman Mélonin Noumonvi, in the semifinals but still successfully grabbed a bronze medal.

In the bronze-medal match, Kajaia faced former world champion and home favourite Balázs Kiss.