Mostly be the boss with quiet restraint (5)
I believe the answer is:
leash
'restraint' is the definition.
(leash is a kind of restraint)
'mostly be the boss with quiet' is the wordplay.
'mostly' means to remove the last letter.
'be the boss' becomes 'lead'.
'with' means one lot of letters go next to another.
'quiet' becomes 'sh'.
'lead' with its last letter taken off is 'lea'.
'lea'+'sh'='LEASH'
(Other definitions for leash that I've seen before include "Rope or chain restraint" , "Restraint for a dog" , "Line for holding dog" , "Restraining strap for dog" , "Strap for holding a dog while walking" .)