Shut up after a firm “Get work” (4)
I believe the answer is:
coop
'shut up' is the definition.
(thesaurus)
'a firm get work' is the wordplay.
'a firm' becomes 'co' (a firm is a company).
'get' says to put letters next to each other.
'work' becomes 'op' (abbreviation for opus).
'co'+'op'='COOP'
'after' is the link.
(Other definitions for coop that I've seen before include "Birdcage" , "Hens in this" , "Cage for poultry" , "box of chickens" , "Store" .)