Awful slut's sexual desire (4)
I believe the answer is:
lust
'sexual desire' is the definition.
(lust is a kind of sexual desire)
'awful slut's' is the wordplay.
'awful' indicates anagramming the letters.
'slut' with letters rearranged gives 'LUST'.
(Other definitions for lust that I've seen before include "Deadly sin of extreme passion" , "Passionate desire" , "Lecherousness" , "Intense sexual desire, a deadly sin" , "Strong sexual desire" .)