Real big name turned up in story (8)
I believe the answer is:
tangible
'real' is the definition.
('tangible' can be similar in meaning to 'real')
'big name turned up in story' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'turned up' is a reversal indicator.
'in' means one lot of letters goes inside another.
'story' becomes 'tale' ('tale' can be a synonym of 'story').
'big'+'n'='bign'
'bign' back-to-front is 'ngib'.
'ngib' placed inside 'tale' is 'TANGIBLE'.
(Other definitions for tangible that I've seen before include "Clear and definite, can be touched" , "Palpable" , "Material" , "Concrete - bleating (anag)" , "Having real substance" .)