Admit to 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' indicates an anagram.
'won' with letters rearranged gives 'OWN'.
'to being' acts as a link.
(Other definitions for own that I've seen before include "Posses" , "Acknowledge" , "Allow" , "Have in one's possession" , "Be in legal possession of (3)" .)