If you are applying for undergraduate studies (first cycle) for the first time, you will have to submit your application usually by the end of July or the beginning of August of the same year you will be starting your studies.
Undergraduate (first cycle) and graduate students (second and third cycle)
Applications are usually submitted within the first fortnight of each academic semester. In Greece the fall semester starts on September 1 and lasts for 15 weeks, i.e., until mid-December. The spring semester starts on February 1 and ends in mid-May.