Studio had story right (7)
I believe the answer is:
atelier
'studio' is the definition.
(atelier is a kind of studio)
'had story right' is the wordplay.
'had' becomes 'ate' (e.g. I had an ice cream).
'story' becomes 'lie' (story can mean a fabrication).
'right' becomes 'r' (abbreviation).
'ate'+'lie'+'r'='ATELIER'
(Other definitions for atelier that I've seen before include "Artist's studio (French)" , "Designer's workshop" , "Tie earl up in the artist's place" , "I relate to workshop used by artist" , "Artist's workroom" .)