The UK is in the course of issuing various notices of what happens in the unlikely event that the UK leaves the EU with a No Deal.
Driving in the EU - https://www.gov.uk/government/publications/driving-in-the-eu-if-theres-no-brexit-deal/driving-in-the-eu-if-theres-no-brexit-deal
Please remember if you live in Cyprus permanently you must convert your driving licence to a Cypriot one regardless of whether there is a Deal or No Deal. This must be done before 29 March 2019. After this date, if you are here permanently and still have your UK licence, it is not known at this stage if Cyprus will ask you to take a new driving test.
If you return to the UK, will be able to re-exchange your Cyprus driving licence for a UK licence.
The Cypriot driving licence will be valid if you drive in the UK on your visits there.