Chase, follow (6)
I believe the answer is:
pursue
I believe this clue is a double definition.
'chase' is the first definition.
(I know that chase is a kind of pursue)
'follow' is the second definition.
(to pursue is to follow or chase)
(Other definitions for pursue that I've seen before include "Engage in or chase after" , "Chase, run after" , "Follow, chase" , "Try to win" , "Be engaged in - hunt" .)