Slim girl's first obsession (5)
I believe the answer is:
'obsession' is the definition.
'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'.
(Other definitions for thing that I've seen before include "An unnamed object or item" , "Affair - matter" , "Individual object" , "Object, artefact" , "Inanimate object" .)