Hi,
Yes, you can work remotely for a UK employer, while being a resident of Cyprus. You would need to report and pay tax in Cyrpus on the UK income.
If you do not need to submit tax returns in the tax year you leave the UK, you should complete form P85 to advise that you are leaving the UK, but will remain employed by a UK employer. You can see information here:
Get your Income Tax right if you're leaving the UK
Thank you.