[3] Moistrapishvili made his senior debut for Telavi in 2020 while on loan there, in a 1–1 draw against FC Locomotive Tbilisi, coming on as a 69th-minute substitute for Tsotne Mosiashvili.
[4] During his loan spell there he would record one goal in 12 appearances in all competitions, the winner in a 2–1 win over Chikhura Sachkhere in November 2020.
[5] When he returned to Dinamo Tbilisi he finally broke into the first team and made his debut in February 2021 in a 1–1 draw against Samgurali coming on as a 79th-minute substitute for Anzor Mekvabishvili.
Moistrapishvili scored 7 goals and recorded 8 assists to help the side to the league title, gaining attention from top European teams such as Sassuolo.
[8] On 5 September 2023, Moistsrapishvili joined Challenger Pro League club Beveren on a season-long loan with the option to make the transfer permanent.