Admit having won somehow on a horse (3,2)
I believe the answer is:
own up
'admit' is the definition.
(I know that own up is a more specific form of the action concede)
'won somehow on a horse' is the wordplay.
I cannot quite understand how this works, but
an anagram of 'won' is 'own' which is present in the answer.
The remaining letters 'up' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'having' acts as a link.
Can you help me to learn more?
(Other definitions for own up that I've seen before include "Admit to wrongdoing" , "Come clean (about wrongdoing)" , "Confess, acknowledge fault" , "Accept responsibility" , "be honest" .)