Old tragedian initially greeting play (7)
I believe the answer is:
othello
'play' is the definition.
(play by William Shakespeare)
'old tragedian initially greeting' is the wordplay.
'initially' suggests taking the first letters.
'greeting' becomes 'hello' (hello is a kind of greeting).
The initial letters of 'old tragedian' is 'ot'.
'ot'+'hello'='OTHELLO'
(Other definitions for othello that I've seen before include "Shakespeare tragedy" , "Jealous character" , "Hello to Shakespeare's Moor" , "Shakespeare play set in Venice/Cyprus" , "Shakespearean Moor" .)