Quiet existence of composition (5,4)
I believe the answer is:
still life
'composition' is the definition.
(I've seen this before)
'quiet existence' is the wordplay.
'quiet' becomes 'still' (similar in meaning).
'existence' becomes 'life' (being alive).
'still'+'life'='STILL-LIFE'
'of' is the link.
(Other definitions for still life that I've seen before include "Picture" , "Painting genre" , "Painting of a bowl of fruit, perhaps?" , "work of art" , "Painting of inanimate things like fruit or flowers" .)