Stamou is a product of the youth academies of Iraklis and signed his first professional contract for the club in the summer of 2010. He debuted in the Superleague debut during a 0–0 home draw against Kerkyra. In the end, he managed to make 3 league appearances for the club.
PAOK
On 29 July 2011, Stamou signed a three-year contract with PAOK, after he was released from Iraklis. However, due to a series of injuries and subsequent operations, he failed to make his debut in the 2011–12 season. In January 2013 Stamou was loaned out to Kerkyra to get some playing time. He debuted for the club on 20 January 2013 in an away match against Skoda Xanthi. He totally appeared in 7 league matches for the club and in one cup match. Stamou returned to PAOK in the following summer. In July 2014 he was released by PAOK.
Return to Iraklis
On 29 July 2014 Stamou returned to Iraklis by signing a two-year contract.