How can EU citizen and non-EU spouse establish permanent residency in Greece?

Please be advised that your wife, as a Cypriot citizen (a European state's citizen), has the right to move and relocate to any EU country and apply for the respective residence permit issuance depending on the reason of relocation. Following her residency permit application, you are entitled based on family reunification provisions for your residence permit as a family member of a Greek permanent residency holder. Since you keep now a resident permit of Cyprus under expiration, it would be advisable to enter Greece before the expiration date due to the existing travel restrictions for non-holders of a European residence permit and start the process.

In Greece, if you still have an establishment, you could apply for 5-year residency due to your marriage.