Hi,
No you won't have problem. You can install the CleanMart to any other up&running domain as long as you remove the CleanMart form the old domain.
Your current allowed domain is: moXXXXri.gr
What is the new domain? (if you don't want to share your new domain in our forum, please email it to This email address is being protected from spambots. You need JavaScript enabled to view it.) Let me add this new domain to your profile so you won't have problem with licensing.
Regards.