There are various synonyms for the phrase "raise the hunt." Some of the most common ones include "start the chase," "initiate the pursuit," "begin the search," and "commence the hunt." Other synonyms include "set off in pursuit," "embark on the chase," "kick off the hunt," and "launch the pursuit." All of these synonyms convey the same idea of starting a hunt or chasing after something, whether it be an animal, an object, or a person. These phrases can be used interchangeably depending on the context and tone of the conversation or written piece.