I've been to Cyprus (Paphos) several times and always take a spinning rod for fishing in the sea. Usually fish off breakwaters using bread or limpets gathered off the rocks for bait. The species of fish you catch are usually small wrasse, the one exception I had was a 6lb grey mullet that I took on floating bread flake, what a scrap that put up.
I've never tried fly fishing in the sea at Paphos mainly because there is usually quite a breeze blowing off the sea making casting difficult and possibly hazardous. I believe that there are inland reservoirs that contain fish but wether there are any species that respond to fly I don't know.
There are rivers in the Troodos Mountains which may contain game fish. The tourist information office in Paphos will probably have details.
The locals who fish in the sea from the shore use long poles and seem to concentrate on catching small fish .
I'm going back to Paphos in September, the spinning rod and tackle will be in my suitcase