Slim girl's first obsession (5)
I believe the answer is:
thing
'obsession' is the definition.
(thesaurus)
'slim girl's first' is the wordplay.
'slim' becomes 'thin' ('thin' can be a synonym of 'slim').
'first' suggests taking the first letters.
The initial letter of 'girls' is 'g'.
'thin'+'g'='THING'
(Other definitions for thing that I've seen before include "An unnamed object or item" , "Affair - matter" , "Individual object" , "Object, artefact" , "Inanimate object" .)