Zambazis began playing soccer at the age of six with Olympic Flame SC.

[8] In August 2014, Zambazis signed with Greek Football League club Iraklis.

On October 29, 2015, Zambazis made his professional debut for Iraklis in a Greek Football Cup match against PAS Giannina.

In November 2011, he made his debut in the Canadian national program, attending a Canada U15 identification camp.

[1] In February 2016, Zambazis played with the Greece U19 in two friendly games against the Czech Republic U19.