Find a Climbing Partner/Belayer
Alternatively, you might have success contacting one of the (few) climbing walls on the island.
If you decide to simply turn up at a crag/sector "on-spec" hoping to hook up with someone then your best chance is the Diarizos/Kourtelorotsos sector on a Saturday/Sunday. You might also have a (somewhat smaller) chance of meeting climbers at the Gerakopetra or Garga Suyu sectors during the weekend (or public holidays). Any other sectors or days then you will have to be pretty lucky to meet anyone.
If you are after a paid guide or belayer then drop the admin an email at firstname.lastname@example.org and we might be able to put you in touch with the most appropriate person (Note that cyprusrocks does not offer a commerical guiding service itself).
It is worth noting that whatever option you choose, that you will have more luck in hooking up if you have your own transport and if you are looking for sport climbing opportunities rather than traditional or bouldering.
If you get totally stuck then feel free to drop the admin an email at email@example.com who might be able to give further help, or might be themselves available for climbing.