Besis was born in Kokkinia, Piraeus, on November 24, 1940. He played for Proodeftiki from the 1956 until the 1962 season. During the summer of that year, Olympiakos offered their Piraeus neighbours cash plus five players (among them Kyriakos Kalkitanidis and Yiannis Frantzis) to obtain his services. Besis played for Olympiakos in 19 games in 1963 and was relegated to the bench. Eventually, he was sent back to Proodeftiki where he played until the 1971 season. Afterwards, he also played for Paniliakos, Ionikos and Hephaestus Nikaia.
Despite his years on the bench, Besis made a total of 205 appearances in the Alpha Ethniki.