Shut up firm having little work (4)
I believe the answer is:
coop
'shut up' is the definition.
(thesaurus)
'firm having little work' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'having' says to put letters next to each other.
'little work' becomes 'op'.
'co'+'op'='COOP'
(Other definitions for coop that I've seen before include "Birdcage" , "pound" , "Pen" , "Cage for poultry" , "box of chickens" .)