New cheese slices provided cut for easy digestion (2,5)
I believe the answer is:
in brief
'cut for easy digestion' is the definition.
(something 'in brief' is cut down or simplified)
'new cheese slices provided' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'cheese' becomes 'brie' (Brie is an example).
'slices' is an insertion indicator (some letters slice into others).
'provided' becomes 'if' (eg 'provided it's sunny' means 'if it's sunny').
'n'+'brie'='nbrie'
'nbrie' inserted within 'if' is 'IN BRIEF'.
(Other definitions for in brief that I've seen before include "To cut a long story short" , "ungarnished?" , "Where barrister finds the facts" , "quickly" , "shortly" .)