Authentic German playwright, not British (4)
I believe the answer is:
echt
'authentic' is the definition.
(I've seen this before)
'german playwright not british' is the wordplay.
'german playwright' becomes 'brecht' (Bertolt Brecht, 1898-1956).
'not' suggests deleting specific letters.
'british' becomes 'br' (abbreviation for British).
'brecht' with 'br' taken away is 'ECHT'.
(Other definitions for echt that I've seen before include "Genuine (Ger.)" , "Genuine -- honest" , "German's real" , "True" , "Authentic (from German)" .)