Initiate story for grandson, perhaps (5,8)

I believe the answer is:

blood relation

'for grandson perhaps' is the definition.
(grandson is a type of relative)

'initiate story' is the wordplay.
'initiate' becomes 'blood' (blood can mean to initiate someone in an activity).
'story' becomes 'relation' (relation is a kind of story).
'blood'+'relation'='BLOOD RELATION'

(Another definition for blood relation that I've seen is " Relative by birth".)

I've seen this clue in The Telegraph.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.