If you own a property here you must have a local will. Even then if you die your property still has to go through probate but if you have a will it is much faster and less complicated.
Go to a good local solicitor to have the will drawn up, they will then go to the Courts with you where the will is stamped and a copy lodged at the courts.
Contrary to what people are told you dont strictly need 2 wills. Probate of your uk will which may concern you world wide assets may be "resealed" in Cyprus. It's quicker though to carry out probate with a will made in Cyprus and less costly. BUT youve got to be sure that your uk will doesnt contrdict your UK willl particularly if you have a uk will drawn up after a cyprus will. If you can get a proper estate practitioner to draw you up a will. My one has trust provisions in it an survivorship clauses..which amazingly dont exist in some one page copy paste so called wills that Ive been shown by some friends on the island. Give my lawyer Stelios Stylianou in Nicosia a call im sure hell point you in the right direction. His details are on his firms web page on Ns-lawyers.
Hope Ive been useful oh and by the way be careful who you out down as an executor of your will in Cyprus if its a lawyer he/shes allowed a percentage of the estate!