Drink brand keeping variety quiet (4,5)
I believe the answer is:
milk shake
'drink' is the definition.
(milk shake is a kind of drink)
'brand keeping variety quiet' is the wordplay.
I cannot quite understand how this works, but
'variety' could be 'ilk' (ilk is a kind of variety) and 'ilk' is found within the answer.
'quiet' could be 'sh' (both can be said to tell someone to be quiet) and 'sh' is found in the answer.
'brand' could be 'make' (synonyms) and 'make' is found in the leftover letters.
No letters remain.
This explanation may well be incorrect...
(Other definitions for milk shake that I've seen before include "Cold whisked drink" , "Dairy/fruit drink" , "Dairy drink" , "Frothy mixed drink" .)