Daughter's first greasy napkin (5)
I believe the answer is:
doily
'napkin' is the definition.
'daughter's first greasy' is the wordplay.
'first' suggests taking the first letters.
'greasy' becomes 'oily' ('oily' can be a synonym of 'greasy').
The initial letter of 'daughters' is 'd'.
'd'+'oily'='DOILY'
(Other definitions for doily that I've seen before include "Lace mat" , "Decorative mat" , "Ornamental mat for plate" , "Paper mat" .)