Dirty rim of mug used for a brew (6)
I believe the answer is:
smudge
'dirty' is the definition.
(I've seen this before)
'rim of mug used for a brew' is the wordplay.
'rim of' says to hollow out the word (remove centre letters) (only the letters at the edges or rims of the word).
'for a brew' is an anagram indicator (letters brewed or mixed up).
'mug' with its middle removed is 'mg'.
'mg'+'used'='mgused'
'mgused' anagrammed gives 'SMUDGE'.
(Other definitions for smudge that I've seen before include "Soil - daub" , "Smeared blot" , "Choking smoke" , "A blemish made by dirt" , "A smeared mark or stain" .)