Girl Friday. No cook (3)
I believe the answer is:
ida
'girl' is the definition.
(I know that Ida is a female given name)
'friday no cook' is the wordplay.
'no' is a deletion indicator.
'cook' becomes 'fry' (frying is a type of cooking).
'friday' with 'fry' taken away is 'IDA'.
(Other definitions for ida that I've seen before include "Princess in a Gilbert and Sullivan comic opera" , "Name of girl or mountain" , "'Princess - - ' (G & S)" , "The girl for Dai" , "Girl's name; aid (anag.)" .)