Lack a young woman (4)
I believe the answer is:
miss
I believe this is a double definition.
'lack' is the first definition.
(I know that lack can be written as miss)
'a young woman' is the second definition.
(title for a young woman)
(Other definitions for miss that I've seen before include "Agatha Christie's detective" , "Fail to perceive" , "Fail to hit (the target)" , "Lass" , "Fail to meet - girl" .)