Company with little work is to shut up (4)
I believe the answer is:
coop
'is to shut up' is the definition.
(thesaurus)
'company with little work' is the wordplay.
'company' becomes 'co' (abbreviation).
'with' 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 "Pen" , "pound" , "Birdcage" , "Cage for poultry" , "Hens in this" .)