After the purchase of the property, your lawyer needs to register the property as your property in the Office of Land Registry, make sure that all the fees related to the purchase are paid, and complete all the processes for the ownership of the property.  

As a second step, your accountant needs to fill E9 form to register that you paid your taxes and the property belongs to you. 

Later on, if you are going to live in the property that you bought. You need

1. To register the electrometer under your name and get electricity service connected.
2. To register the water meter under your name and get water service connected.
3. To get the internet connected.
4. If needed, to start the process for natural gas connection.
5. To buy the furniture that you need and install them.
6. If needed, renovation in kitchen and bathroom, painting, and installment of security systems.
7. To let the building management that you will be paying the common expenses and attending the building meetings. 
8. To get the keys to the common areas of the building and the building code from the building manager. We advise you to read the regulations.
9. To ensure your property in terms of thievery, fire, and earthquake. Beware that the insurance companies in Greece do not want to insure the properties that are built before the 1960s. 
10. To have health insurance for the application of a residence permit.
11. If you are going to spend time in Greece with your family, to have family health insurance as a package.