Follow to the end (4)
I believe the answer is:
tail
I believe this clue is a double definition.
'follow' is the first definition.
(both can mean to chase or pursue)
'the end' is the second definition.
(tail is a kind of end)
'to' acts as a link.
(Other definitions for tail that I've seen before include "Private investigator" , "Dog - or part of one" , "Follow; end part" , "Hindmost part" , "Follow closely - taper (off)" .)