Playwright's single book despatched unfinished (5)
I believe the answer is:
ibsen
'playwright's' is the definition.
(Ibsen is an example)
'single book despatched unfinished' is the wordplay.
'single' becomes 'i' (one).
'book' becomes 'b'.
'despatched' becomes 'sent' (I've seen this before).
'unfinished' means to remove the last letter.
'sent' with its final letter removed is 'sen'.
'i'+'b'+'sen'='IBSEN'
(Other definitions for ibsen that I've seen before include "Noted Norwegian playwright" , "Norwegian dramatist and poet" , "Hedda Gabler author" , "foreign author" , "famous Norwegian" .)