What is the official called in bullfighting?

Answer 1

There is no 'referee' in a bullfight. There is, however, a judge of the bullfight called presidente who sits high in the bullring and he controls the fight. He is usually a government official and is usually advised by a retired matador or other knowledgeable person. He signals the changes of the terceos (acts) of the bullfight and awards trophies (ears, tail of the bull) to the matador. His commands are sent via a trumpeter to the participants of the fight. Each short Trumpet melody has a specific meaning.

Answer 2

El Presidente is the official who calls the shots in the bullring, assisted usually by a former torereo.