Poor girl's obsession? (5)
I believe the answer is:
thing
'obsession?' is the definition.
(I've seen this in other clues)
'poor girl's' is the wordplay.
'poor' becomes 'thin' (I've seen this in other clues).
'girl' becomes 'g'.
'thin'+'g'='THING'
(Other definitions for thing that I've seen before include "Object; gadget" , "Obsession" , "Individual unit" , "A creature" , "Article" .)