Dame Judith and her beheaded kid (8)
I believe the answer is:
anderson
'dame judith' is the definition.
(I've seen this in another clue)
'and her beheaded kid' is the wordplay.
'beheaded' means to remove the first letter (the head of the word is removed).
'kid' becomes 'son' (male child).
'her' with its first letter taken away is 'er'.
'and'+'er'+'son'='ANDERSON'
(Other definitions for anderson that I've seen before include "Sir John -, gave name to WW 2 air-raid shelter" , "Lindsay ____, English film director, d. 1994" .)