An island-restricted permission does not authorise travel to Athens or another part of mainland Greece. Taking a domestic flight from the island does not change that restriction. If the itinerary includes an Athens hotel, a return flight from Athens or onward travel to another Schengen country, you need permission or an applicable exemption covering the whole journey. First check any existing visa’s territorial validity, dates, entry allowance and permitted stay. If a new application is necessary, determine the responsible authority under the main-destination rules. Confirm your circumstances with the competent Greek consular authority before buying fixed tickets.