Scraggy girl’s first obsession (5)
I believe the answer is:
thing
'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').
'thin'+'g'='THING'
(Other definitions for thing that I've seen before include "Article" , "A creature" , "Unspecified object" , "Object; gadget" , "Individual unit" .)