Lady, mistress of grand house, cutting the chat (6)
I believe the answer is:
elaine
'lady' is the definition.
(woman's name)
'mistress of grand house cutting the chat' is the wordplay.
'mistress of grand house' becomes 'chatelaine' (term for a woman in charge of a large house).
'cutting' suggests deleting specific letters.
'chatelaine' with 'chat' taken away is 'ELAINE'.
(Other definitions for elaine that I've seen before include "Name" , "Woman" , "Girl" , "-- Paige, singer" , "-- Paige, singer/actress" .)