Lord's fib disheartened Grace (5)
I believe the answer is:
liege
'lord's' is the definition.
(feudal term for a superior)
'fib disheartened grace' is the wordplay.
'fib' becomes 'lie' (a fib is a lie).
'disheartened' suggests removing the centre (the middle or heart is removed).
'grace' with its centre taken out is 'ge'.
'lie'+'ge'='LIEGE'
(Other definitions for liege that I've seen before include "World War one battle site" , "Feudal (lord); vassal" , "Chieftain" , "Vassal; city in Belgium" , "Bound to render feudal service" .)