Many a mug has quality (5)
I believe the answer is:
class
'quality' is the definition.
(I have seen 'High quality' mean 'class' so perhaps 'quality' could also mean 'class')
'many a mug' is the wordplay.
'many a' becomes 'cl' (I am not sure about this - if you are sure you should believe this answer much more).
'mug' becomes 'ass' (I've seen this before).
'cl'+'ass'='CLASS'
'has' acts as a link.
(Other definitions for class that I've seen before include "Where one learns" , "Stylish; lesson" , "Teaching group" , "period" , "Category; form" .)