The woman would shortly peel off (4)
I believe the answer is:
shed
'peel off' is the definition.
(thesaurus)
'the woman would shortly' is the wordplay.
'the woman' becomes 'she' (I've seen this before**).
'shortly' says to take the final letters.
The final letter of 'would' is 'd'.
'she'+'d'='SHED'
(Other definitions for shed that I've seen before include "Abandon" , "Separate" , "Cast, wooden building" , "storage building" , "lost" .)