Iakobishvili competed in the men's freestyle 65 kg event at the 2016 Summer Olympics in Rio, where he reached the quarterfinals and placed tenth.

He represented Georgia at the 2016 Summer Olympics in Rio and competed in the men's freestyle 65 kg event, where he reached the quarterfinals and placed tenth.

[12][13] Iakobishvili switched to the 70 kg weight class for the 2018 European Championships in Kaspiysk, where he won a bronze medal.

[14] That same year, he won the gold medal in the freestyle 70 kg event at the Tbilisi Grand Prix and Poland Open.

In 2021, Iakobishvili won a bronze medal in the freestyle 70 kg event at the World Championships in Oslo.