Ale drunk with quiet restraint (5)
I believe the answer is:
leash
'restraint' is the definition.
(leash is a kind of restraint)
'ale drunk with quiet' is the wordplay.
'drunk' indicates anagramming the letters.
'with' means one lot of letters go next to another.
'quiet' becomes 'sh'.
'ale' with letters rearranged gives 'lea'.
'lea'+'sh'='LEASH'
(Other definitions for leash that I've seen before include "Animal restraint" , "Strip for leading, a dog say" , "Rope to control dog" , "Restraining strap for dog" , "Rope or chain restraint" .)