Badger and horse (3)
I believe the answer is:
nag
This clue is a double definition.
'badger' is the first definition.
(both can mean to annoy or complain at)
'horse' is the second definition.
(term for an old horse)
'and' is the link.
(Other definitions for nag that I've seen before include "plague" , "Worry; old horse" , "Harry" , "its head to name the pub" , "Old Arab maybe" .)