Cap removed from playwright put in grave (5)
I believe the answer is:
inter
'put in grave' is the definition.
(as in interring a body)
'cap removed from playwright' is the wordplay.
'cap removed from' means to remove the first letter (the top letter or 'cap' is removed).
'playwright' becomes 'pinter' (Harold Pinter).
'pinter' with its first letter taken off is 'INTER'.
(Other definitions for inter that I've seen before include "Send to ground" , "foreign team" , "team from Italy" , "Prefix for between - bury it" , "I rent (anag.)" .)