Chaotic study in need of a clean? (5)
I believe the answer is:
dusty
'in need of a clean?' is the definition.
(something dusty needs to be cleaned)
'chaotic study' is the wordplay.
'chaotic' is an anagram indicator.
'study' anagrammed gives 'DUSTY'.
(Other definitions for dusty that I've seen before include "Ms Springfield" , "In need of a spring clean" , "Mr Miller" , "Dull (like a miller?)" , "Covered in fine particles" .)