Female with new hat and close-fitting dress (6)
I believe the answer is:
sheath
'close-fitting dress' is the definition.
'female with new hat' is the wordplay.
'female' becomes 'she' (I've seen this before).
'with' is a charade indicator (letters next to each other).
'new' indicates an anagram.
'hat' is an anagram of 'ath'.
'she'+'ath'='SHEATH'
'and' is the link.
(Other definitions for sheath that I've seen before include "jacket" , "Protective case for a knife or sword" , "Covering for blade" , "Scabbard" , "Cover protecting" .)