There are a few species mentioned in expanded universe sources as having some sort of legal protection against hunting. According to Galaxy Guide 4: Alien Races, a bird-like predatory species called the elix was rescued from extinction by the Empire when the sun of their homeworld went supernova. Unfortunately, the Empire put the elix on a planet inhabited by a primitive intelligent species who the elix treated as a source of food.
Another book, Creatures of the Galaxy, describes the tresher, another protected bird species. The local government of their home planet prohibited hunting them because of their importance to the planetary ecosystem.