Like Bridget Jones, divulge secrets twice! (9)
I believe the answer is:
singleton
'like bridget jones' is the definition.
(Bridget Jones is single in Helen Fielding's novels)
'divulge secrets twice' is the wordplay.
'divulge secrets' becomes 'sing' (sing can mean to give information to the police).
'twice' becomes 'leton' (I can't explain this - if you can you should believe this answer much more).
'sing'+'leton'='SINGLETON'
(Other definitions for singleton that I've seen before include "could be ace on its own?" , "Eg lonely heart" , "person not in a long-term relationship?" , "in club, maybe, all alone" , "One object only" .)