In hot pursuit (of somebody) American negative informal
The superstar drove off, with paparazzi in hot pursuit.
The thief was running down the street, with several residents in hot pursuit.
The police are in hot pursuit of the bank robber.
following closely behind someone
stop following, stop disturbing
Used to describe the imitation of others' manner or the following of others' guidance.
To go after or follow one anywhere.
You can also use "with someone" before the phrase to refer to who the pursuer is