Pool and chess diverted playwright (9)
I believe the answer is:
sophocles
'playwright' is the definition.
(I've seen this before)
'pool and chess diverted' is the wordplay.
'and' is a charade indicator (letters next to each other).
'diverted' indicates anagramming the letters (letters must be diverted to different positions).
'pool' after 'chess' is 'chesspool'.
'chesspool' with letters rearranged gives 'SOPHOCLES'.
(Other definitions for sophocles that I've seen before include "Ancient Greek tragedian" , "Classical versifier" , "Ancient Greek philosopher" , "One bringing charges" , "Greek dramatist, author of Oedipus Rex" .)