The official language in the republic of Cyprus is Greek Cypriot, which is a dialect of Greek that has been influenced by the large number of different nations that have ruled Cyprus over the centuries. Despite using the same grammar and letters, the Greek Cypriot language uses many Ancient Greek words and other Greek words that are pronounced differently to standard Modern Greek.
However, many Cypriot Greek speakers will know the Standard Greek variations so if you do speak Modern Greek well they will most likely adapt their speaking to Standard Greek so that you can understand them.
Many Cypriots also speak English as it is a sign of sophistication, and as many of the jobs in Cyprus are related to the tourist industry, it is considered a great skill to have in order to get employed. Because of this, you can easily get away without learning any Greek at all, but this is not recommended, as you will reach many limitations with the Cypriot people. By learning a little bit of Greek you will gain the respect of the local people and find that you get that little bit extra added to your vacation.