Play well, trapping Middlesex's opener before tea, say (6)
I believe the answer is:
hamlet
'play' is the definition.
(play by William Shakespeare)
'well trapping middlesex's opener before tea say' is the wordplay.
'well' becomes 'hale' (I've seen this before).
'trapping' indicates putting letters inside.
'opener' says to take the initial letters.
'before' is a charade indicator (letters next to each other).
'tea say' becomes 't' (I've seen this in other clues).
The first letter of 'middlesex' is 'm'.
'hale' enclosing 'm' is 'hamle'.
'hamle'+'t'='HAMLET'
(Other definitions for hamlet that I've seen before include "famous title role" , "tragic role" , "The Dane" , "Shakespearean tragedy" , "(Hero of) play" .)