Appointed grandma to dismiss a chaperone (6)
I believe the answer is:
duenna
'chaperone' is the definition.
(duenna is a kind of chaperone)
'appointed grandma to dismiss a' is the wordplay.
'appointed' becomes 'due'.
'grandma' becomes 'nana' (I've seen this before).
'to dismiss' indicates named letters should be taken away.
'nana' with 'a' taken away is 'nna'.
'due'+'nna'='DUENNA'
(Other definitions for duenna that I've seen before include "Chaperone in Madrid" , "Chaperon to young girl in Spain" , "(Spanish) chaperone" , "Governess, chaperone" , "Iberian chaperone" .)