Granddaughter, perhaps, beginning to read? Joy (8)
I believe the answer is:
relation
'granddaughter perhaps' is the definition.
(granddaughter is a kind of relation)
'beginning to read? joy' is the wordplay.
'beginning to' says to take the initial letters.
'joy' becomes 'elation' (elation is a kind of joy).
The initial letter of 'read' is 'r'.
'r'+'elation'='RELATION'
(Other definitions for relation that I've seen before include "Oriental kind of family connection" , "Kinship; narrative" , "Kinsman; narrative" , "Auntie?" , "Telling" .)