There are numerous synonyms for the phrase "in hot pursuit," which denotes a pursuit or pursuit attempt of a fleeing person, vehicle or object. Some synonyms which come to mind include "in vigorous pursuit," "in relentless pursuit," "in hot pursuit mode," "in chase mode," "in pursuit mode," "on the chase," "on the trail of," "on the hunt for," and "after." These phrases are commonly used in news reports, action movies, and literature to describe a thrilling and ongoing pursuit that often involves high-speed chases and heart-pumping action sequences. In conclusion, although the phrase "in hot pursuit" is commonly used, there are various alternative synonyms that can be used to describe the same situation.