fresh pursuit

Definition from Nolo’s Plain-English Law Dictionary

Also known as "hot pursuit," the chase by police of a person whom police have reason to believe has just committed a crime. In this situation, the officer may arrest the suspect without a warrant. Fresh pursuit also enables an officer to enter another jurisdiction (county or state) to pursue a fleeing suspect (normally, officers' abilities to arrest people are limited to their county and state).

Definition provided by Nolo’s Plain-English Law Dictionary.