Scraggy girl’s first obsession (5)
I believe the answer is:
'obsession' is the definition.
(I've seen this before)
'scraggy girl's first' is the wordplay.
'scraggy' becomes 'thin' (similar in meaning).
'girl's first' becomes 'g' (1st letter of 'girl').
(Other definitions for thing that I've seen before include "Article" , "A creature" , "Unspecified object" , "Object; gadget" , "Individual unit" .)