Local church admitted to previous naivety (9)
I believe the answer is:
innocence
'naivety' is the definition.
(innocence is a kind of naivety)
'local church admitted to previous' is the wordplay.
'local' becomes 'inn' (local can mean someone's local pub).
'church' becomes 'CE' (abbreviation for Church of England).
'admitted to' indicates putting letters inside.
'previous' becomes 'once' (once can mean 'previously').
'ce' going into 'once' is 'ocence'.
'inn'+'ocence'='INNOCENCE'
(Other definitions for innocence that I've seen before include "Moral purity" , "simplicity for you!" , "Lack of guilt" , "Honesty" , "Freedom from guilt" .)