Horse is worry, constantly (3)
I believe the answer is:
nag
This clue is a double definition.
'horse' is the first definition.
(term for an old horse)
'worry constantly' is the second definition.
(I've seen this before)
'is' is the link.
(Other definitions for nag that I've seen before include "Equine" , "Persistently worry; horse" , "Hack" , "(Of pain) ache dully; horse (colloq.)" , "Keep worrying" .)