In hot pursuit is a phrase used to describe a situation in which someone is actively chasing or pursuing another person or thing. The term is often used in law enforcement, where it refers to the act of chasing a suspect in order to apprehend them. It can also be used more generally to refer to any situation in which one person or group is actively pursuing another. In this crossword, the solution for the term IN HOT PURSUIT is FOLLOWING, which accurately describes the action of actively pursuing someone or something.