You mean restaurants that serve only vegi food? There are many restaurants that have vegi dishes but I don't think you will find many restaurants serving only vegetarian food.
I only just returned from Paphos, and you are really spoilt for choice with restaurants and there is plenty of vegeterian meals to choose from. Wish I was on a plane going back there since I enjoyed the relaxed and friendly atmosphere so much. Make the most of it because you will feel the same as me when ya return