Study possibly in need of cleaning? (5)
I believe the answer is:
dusty
'in need of cleaning?' is the definition.
(I've seen this before)
'study possibly' is the wordplay.
'possibly' is an anagram indicator.
'study' is an anagram of 'DUSTY'.
(Other definitions for dusty that I've seen before include "Covered in fine powder" , "In need of a spring clean" , "Covered in fine particles" , "Particle-covered" , "Neglected and in need of a clean" .)