Hairdo — skullcap (4)
I believe the answer is:
coif
This clue is a double definition.
'hairdo' is the first definition.
(I know that hairdo can be written as coif)
'skullcap' is the second definition.
(coif is a kind of skullcap)
(Other definitions for coif that I've seen before include "what can be made of lawn?" , "Cap worn by fundamentalist Mormon women: hairstyle" , "Headgear" , "Nun's cap" , "Dress the hair" .)