Fail to include note in part of Bible (4)
I believe the answer is:
omit
'fail to include' is the definition.
(I've seen this before)
'note in part of bible' is the wordplay.
'note' becomes 'mi' (as in 'do re mi').
'in' means one lot of letters goes inside another.
'part of bible' becomes 'ot' (Old Testament abbreviation).
'mi' inserted within 'ot' is 'OMIT'.
(Other definitions for omit that I've seen before include "Exclude - neglect" , "Fail (to do something)" , "by-pass" , "Fail to use" , "Exclude; forget to include" .)