Playwright has right peripheral (7)
I believe the answer is:
printer
'peripheral' is the definition.
(I know that printer is a type of peripheral)
'playwright has right' is the wordplay.
'playwright' becomes 'pinter' (Harold Pinter).
'has' is an insertion indicator.
'right' becomes 'r' (common abbreviation).
'pinter' placed around 'r' is 'PRINTER'.
(Other definitions for printer that I've seen before include "Compositor" , "Producer of reading material" , "who makes an impression" , "Computer peripheral" , "eg Typesetter" .)