Playwright is barely surviving, eating nothing initially (5)
I believe the answer is:
ibsen
'playwright' is the definition.
(Ibsen is an example)
'is barely surviving eating nothing initially' is the wordplay.
'initially' suggests taking the first letters.
The first letters of 'is barely surviving eating nothing' is 'IBSEN'.
(Other definitions for ibsen that I've seen before include "Noted Norwegian playwright" , "'Doll's House' playwright" , "Author of The Master Builder, d. 1906" , "foreign author" , "Norwegian playwright (Peer Gynt)" .)