Stealthy pursuer (7)
I believe the answer is:
stalker
'stealthy pursuer' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for stalker that I've seen before include "Stealthy pursuer" , "One harassing celebrity" , "who follows a celebrity?" , "Tracker" , "Someone following another, sneakily" .)