Go on at a horse (3)
I believe the answer is:
nag
'horse' is the definition.
(term for an old horse)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for nag that I've seen before include "Old Arab maybe" , "Annoy constantly" , "Annoy the old horse persistently" , "Constant worrier" , "Equine" .)