Yes, as an Indian passport holder, you must apply for a visa to Cyprus. Customs officials will always consider your passport and not your residence status in a given country. Since the UK and Cyprus are not Schengen Zone countries, your passport will be checked upon arrival. Once Cyprus implements the Schengen Agreement in the near future, you will still be required to present a passport and a valid visa, because the UK is likely to remain outside of this passport-free travel zone.
