A belated idea to edit book of David's songs (7)
I believe the answer is:
psalter
'book of david's songs' is the definition.
(collection of Psalms - David wrote most of them)
'a belated idea to edit' is the wordplay.
'a belated idea' becomes 'ps' (belated or additional idea in a letter).
'to edit' becomes 'alter' (altering is a kind of editing).
'ps'+'alter'='PSALTER'
(Other definitions for psalter that I've seen before include "Book of religious songs" , "Cherub-like" , "Book for church use" , "Book used in church" , "Church chanting book" .)