The word hunt serves as both a noun ("the act, the practice, or an instance of hunting") and a verb ("to pursue for food or in sport").
The noun has been dated to the early 12th century, from the verb hunt. Old English had huntung, huntoþ.
The meaning of "a body of persons associated for the purpose of hunting with a pack of hounds" is first recorded in the 1570s. "The act of searching for someone or something" is from about 1600.