Yes you do have to make your own arrangements and pay for transporting pets to Cyprus , if it is a cat or dog and you are posted to the WSBA then I can reccommend http://barc-cyprus.org/html/import.html who are very helpful and can organise the whole thing for you .
I know this is a bit late but I used PAR AIR from colchester, they travelled to Germany picked my dog up and got him out no problem.
However, be careful of the Cypriots as they charge you to take the dog into the country and they will only release dog/pet to you once you pay a few hundred pounds to a vet who will come out and say " Yes thats a ????" bleeding rip off and when you then get your dog home another vet has to come out give a rabies jab and charge for that. I caught the bastard out because he said he give a shot when I actually caught him putting in a needle but no liquid. Big row, kicked him out and got another vet.
Dont let this put you off but watch everything the vets do.