Person with cool, close-fitting attire (6)
I believe the answer is:
bodice
'close-fitting attire' is the definition.
(I know that bodice is a type of close-fitting attire)
'person with cool' is the wordplay.
'person' becomes 'bod' (bod can informally mean a person or body).
'with' says to put letters next to each other.
'cool' becomes 'ice' (icing is a kind of cooling).
'bod'+'ice'='BODICE'
(Other definitions for bodice that I've seen before include "Basque" , "Corset" , "Top of a dress above the waist" , "Sexually explicit historical novel" , "Stays" .)