Writer admitting current work is a cinematic life story (6)
I believe the answer is:
biopic
'a cinematic life story' is the definition.
(film about someone's life)
'writer admitting current work' is the wordplay.
'writer' becomes 'bic' (kind of pen).
'admitting' means one lot of letters goes inside another (admit can mean to welcome in or accept).
'current' becomes 'I' (symbol for electric current).
'work' becomes 'op' (abbreviation for opus).
'i'+'op'='iop'
'bic' enclosing 'iop' is 'BIOPIC'.
'is' acts as a link.
(Other definitions for biopic that I've seen before include "Film of someone's life" , "Film based on famous person's life" , "Celebrity film" , "Gandhi, say" , "... E.g. Gandhi" .)