Czech Republic is part of the European Union, and UK citizens can travel there without a visa, however if you wish to work or remain in Cyprus for more than 30 days or settle in the Czech Republic, you will be required to register with the Czech Foreign Police.
Your passport should be valid for the duration of your stay.
Visa Not Required
Citizens of the United Kingdom do not require a visa to travel to the Czech Republic as they have Indefinite Leave To Remain. This means that you can travel freely into and out of the country. Please check below for any document requirements that may be needed including specific passport information.