Drink noisily, not softly, and speak without distinction (4)
I believe the answer is:
slur
'speak without distinction' is the definition.
(as in slurring one's speech)
'drink noisily not softly' is the wordplay.
'drink noisily' becomes 'slurp' (I've seen this before).
'not' indicates named letters should be taken away.
'softly' becomes 'p' (short for piano, musical term for softly).
'slurp' with 'p' taken out is 'SLUR'.
'and' acts as a link.
(Other definitions for slur that I've seen before include "Slight - aspersion" , "Disparagement" , "Slight sound" , "Slight, insult" , "Aspersion - speak indistinctly" .)