Cosmetic comments that are impertinent don’t go away (8)
I believe the answer is:
lipstick
'cosmetic' is the definition.
(I know that lipstick is a type of make-up)
'comments that are impertinent don't go away' is the wordplay.
'comments that are impertinent' becomes 'lip' (as in giving someone lip).
'don't go away' becomes 'stick' (if something sticks it doesn't go away or leave).
'lip'+'stick'='LIPSTICK'
(Other definitions for lipstick that I've seen before include "Type of paint" , "Item of make-up equipment" , "Colour applied to the mouth" , "Type of cosmetic" , "Cosmetic used to colour around the mouth" .)