Employ in quiet exhibition space (6)
I believe the answer is:
museum
'exhibition space' is the definition.
(where things are exhibited)
'employ in quiet' is the wordplay.
'employ' becomes 'use' (synonyms).
'in' indicates putting letters inside.
'quiet' becomes 'mum' (I've seen this in another clue).
'use' inserted into 'mum' is 'MUSEUM'.
(Other definitions for museum that I've seen before include "Building where objects of interest are displayed" , "Building holding objects of historical or scientific interest" , "The Hermitage" , "The Ashmolean, for example" , "Sue mum (anag.)" .)