That lady would lose hair (4)

I believe the answer is:

shed

I'm a little stuck... Click here to teach me more about this clue!

'lose hair' is the definition.
'shed' can be an answer for 'lose' (I've seen this before). I am unsure of the 'hair' bit.

'that lady would' is the wordplay.
'that lady' becomes 'she' (I've seen this in another clue).
'would' becomes 'd' (I've seen this in other clues).
'she'+'d'='SHED'

Can you help me to learn more?

(Other definitions for shed that I've seen before include "Drop; outhouse" , "Basic building" , "Barn" , "Simple building; discard" , "Take off in hut?" .)

I've seen this clue in the Sydney Morning Herald.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.