I’m exasperated about nasty old lady (3)

I believe the answer is:

hag

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

'old lady' is the definition.
(thesaurus)

I don't understand how the remainder of the clue works.

(Other definitions for hag that I've seen before include "Witch or ugly old woman" , "Crone" , "Old witch-like woman" .)

I've seen this clue in The Sunday Times.

Want a hint initially instead of a full solution? Install my app