Admit being won over (3)
I believe the answer is:
own
'admit' is the definition.
(own can mean to admit or acknowledge)
'won over' is the wordplay.
'over' is an anagram indicator.
'won' anagrammed gives 'OWN'.
'being' acts as a link.
(Other definitions for own that I've seen before include "Be in legal possession of (3)" , "Keep" , "Possess or confess" , "Possess - recognise - admit" , "Have in one's possession" .)