Stain starts to show lightly under rug (4)
I believe the answer is:
slur
'stain' is the definition.
(I've seen this before)
'starts to show lightly under rug' is the wordplay.
'starts to' suggests taking the first letters.
The first letters of 'show lightly under rug' is 'SLUR'.
(Other definitions for slur that I've seen before include "Pronounce indistinctly with each sound running into the next" , "libel" , "Aspersion - speak indistinctly" , "Speak indistinctly, as a drunk might" , "Pronounce indistinctly or speak ill of" .)