Leave out note in books (4)
I believe the answer is:
omit
'leave out' is the definition.
('omit' can be a synonym of 'leave out')
'note in books' is the wordplay.
'note' becomes 'mi' (as in 'do re mi').
'in' is an insertion indicator.
'books' becomes 'ot' (Old Testament).
'mi' going within 'ot' is 'OMIT'.
(Other definitions for omit that I've seen before include "Leave out or overlook" , "Leave out or exclude" , "Leave out or fail to do" , "Fail to use" , "Leave out, perhaps in error" .)