Snitching about fool (3)
I believe the answer is:
nit
'fool' is the definition.
(both can mean a stupid person)
'snitching about' is the wordplay.
'about' says the answer is hidden in the clue (the clue goes around or about the answer).
'NIT' is hidden within 'snitching'.
(Other definitions for nit that I've seen before include "Louse; fool" , "Egg of a head louse" , "Louse's egg; idiot" , "Cause of much head-scratching" , "Egg of a louse (3)" .)