Starts to wash incredibly grimy rug (3)
I believe the answer is:
wig
'rug' is the definition.
('rug' is an informal term for a wig)
'starts to wash incredibly grimy' is the wordplay.
'starts to' suggests taking the first letters.
The initial letters of 'wash incredibly grimy' is 'WIG'.
(Other definitions for wig that I've seen before include "False head of hair" , "Disguise for baldness" , "rug" , "Artificial hair" , "carpet" .)