Very adult books saw covers getting interest (9)
I believe the answer is:
advantage
'interest' is the definition.
(thesaurus)
'very adult books saw covers' is the wordplay.
'very' becomes 'v' (abbreviation).
'adult' becomes 'a' (abbreviation).
'books' becomes 'NT' (abbreviation for New Testament).
'saw' becomes 'adage' (saw can mean a proverb or saying).
'covers' means one lot of letters goes inside another.
'v'+'a'+'nt'='vant'
'vant' going within 'adage' is 'ADVANTAGE'.
'getting' is the link.
(Other definitions for advantage that I've seen before include "Edge, head start" , "Superior or more favourable position" , "Asset" , "Favourable circumstance" , "Benefit, profit" .)