[2] Kvesić won the silver medal in the men's kumite +84 kg event at the 2019 European Games held in Minsk, Belarus.

[3][4] In 2021, he won one of the bronze medals in the men's +84 kg event at the World Karate Championships held in Dubai, United Arab Emirates.

[5] Kvesić won the gold medal in the men's kumite +84 kg event at the 2022 European Karate Championships held in Gaziantep, Turkey.

[8][9] He won the silver medal in the men's kumite +84 kg event at the 2022 World Games held in Birmingham, United States.

[10][11] Kvesić won one of the bronze medals in the men's +84 kg event at the 2023 European Karate Championships held in Guadalajara, Spain.