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' with letters rearranged gives 'OWN'.
'being' is the 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" .)