As a Greek golden visa holder, how can I establish a company for the purpose of renting our properties in Greece without a director with EU citizenship?

The only way to achieve that is by establishing in Greece a branch of a foreign company. If you choose to form a Greek company, it is necessary that the director of the company is either a Greek or EU citizen or a third-country citizen who holds a residence permit that gives access to business activity (the Golden Visa residence permit does not).

As a Golden Visa holder, you can establish a Greek company under the profile of shareholder. But in order to be the director or the legal representative of the said company, you need a dedicated residence permit. Golden Visa title does not provide you this right. Besides, is it a good idea in terms of taxation aspect the establishment of a company for renting out the properties instead of doing this business as an individual?