Woman's hat lining (4)
I believe the answer is:
caul
'woman's hat lining' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for caul that I've seen before include "Membrane covering an infant's head" , "Membrane sometimes on child's head at birth" , "Membrane covering the head at birth" , "Membrane found on child's head at birth, considered lucky" , "Membrane sometimes on head of new-born baby" .)