Headwear a little bit worn by summer's end (5)
I believe the answer is:
mitre
'headwear' is the definition.
(headwear worn by a bishop)
'a little bit worn by summer's end' is the wordplay.
'a little bit' becomes 'mite' (I've seen this in another clue).
'worn by' means one lot of letters goes inside another (outside letters are worn by those on the inside).
'end' suggests the final letters.
The final letter of 'summer' is 'r'.
'mite' enclosing 'r' is 'MITRE'.
(Other definitions for mitre that I've seen before include "A bishop's tall hat" , "top?" , "Item of headgear" , "Type of joint - bishop's hat" , "Corner joint - bishop's hat" .)