Part of a hat (4)
I believe the answer is:
brim
'part of a hat' is the definition.
('brim' is part of 'hat')
This is all the clue.
(Other definitions for brim that I've seen before include "Edge around a hat" , "'Edge, like that of a hat (4)'" , "Peak (of cap); be very full" , "Lip; part of a hat" , "Lip of a vessel" .)