Verified answer

Are you a Turkish Cypriot planning to live in the northern part of Cyprus? If you have Indefinite Leave to Remain, it will expire once you've been out of the UK for two years.

If you're from the southern part of Cyprus, it has been a member of the EU since May 2004 & you can move freely through the EU & settle where you wish, including the UK without restrictions

http://www.ukvisas.gov.uk/en/doineedvisa/

I think so, but as they are both EU, I don't think getting a new one poses a problem.