Picks up where one stops (7)
I believe the answer is:
arrests
I believe this clue is a double definition.
'picks up' is the first definition.
('arrest' can be a synonym of 'pick up')
'one stops' is the second definition.
(arrest is a kind of stop)
'where' is the link.
(Other definitions for arrests that I've seen before include "Seizes and takes into custody" , "Checks" , "has a heart attack" , "Stops and takes into custody" , "made by police" .)