Not all drink noisily and speak like a drunk (4)
I believe the answer is:
slur
'speak like a drunk' is the definition.
(I've seen this in another clue)
'not all drink noisily' is the wordplay.
'not all' means to remove the last letter (not quite all of it).
'drink noisily' becomes 'slurp' (I've seen this before).
'slurp' with its final letter taken off is 'SLUR'.
'and' is the link.
(Other definitions for slur that I've seen before include "Slight - stain" , "libel" , "making indistinct sound" , "Disparaging comment" , "Discredit, say reputation" .)