Books containing note found in skip (4)
I believe the answer is:
omit
'skip' is the definition.
(I've seen this before)
'books containing note' is the wordplay.
'books' becomes 'ot' (Old Testament).
'containing' indicates putting letters inside.
'note' becomes 'mi' (as in 'do re mi').
'ot' going around 'mi' is 'OMIT'.
'found in' acts as a link.
(Other definitions for omit that I've seen before include "Drop" , "Miss out" , "Leave out or fail to do" , "Leave something out" , "Leave out or overlook" .)