He made his debut on 7 May in the eighth matchday of the Umaglesi Liga championship round against Sioni Bolnisi, netting his side's second goal after coming on as a substitute for Kakhaber Kakashvili in a 2–0 home win.

[2] Kiteishvili scored his first league goal for the club on 3 October 2015, which proved to be the match-winner in a 1–0 home win over Dinamo Batumi.

[5] Being now Dinamo's captain at age 22, he was also recognized as the best player of part II in the 2018 Erovnuli Liga season.

[2] On 31 July 2018, Kiteishvili moved to Sturm Graz in the Austrian Football Bundesliga, where he signed a four-year contract,[7] later extended until the summer of 2024.

[8] He made his debut on 12 August in the third matchday of the domestic league against SKN St. Pölten, coming on as a substitute in the 68th minute for Lukas Grozurek of a 2–0 away loss.