Depends where you'll be living. Paphos has a huge UK community and is like a colony. There is the UKCA which is a organisation in all the major towns of Cyprus for UK citizens. They have trips and coffee mornings, courses and holidays together. The bases offer a wide variety of courses too such as art and flower arranging, horse riding, shooting. There is a reading group in Larnaca at the Academic Book Shop every 1st Thursday of the month. There is yoga too at the American Academy mondays and thursday evenings which is conducted in english. There are playgroups and creches, Little Acorns in Larnaca for instance is English. There may even be a Dutch community so contact the Embassy.
There is a lot happening but depends where you live and what you want to do. Let me know and I'll look into it more if you have a specific interest.