Admit to being won over (3)
I believe the answer is:
'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)" .)