Go on at horse (3)
I believe the answer is:
nag
'horse' is the definition.
(term for an old horse)
I cannot 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 "Scold; inferior horse" , "Ailing horse" , "Poor horse" , "to get on one's back" , "Termagant" .)