Sign ill-tempered woman doesn’t have answer (5)
I believe the answer is:
virgo
'sign' is the definition.
(I know that Virgo is a sign)
'ill-tempered woman doesn't have answer' is the wordplay.
'ill-tempered woman' becomes 'virago' (I've seen this in another clue).
'doesn't have' indicates named letters should be taken away.
'answer' becomes 'a' (abbreviation eg in Q and A).
'virago' with 'a' removed is 'VIRGO'.
(Other definitions for virgo that I've seen before include "Star sign" , "Large constellation -- sign of the zodiac" , "House" , "number of stars" , "A constellation, a cluster" .)