Elizabethans rejected laziest playwright (5)
I believe the answer is:
behan
'playwright' is the definition.
(I've seen this before)
'elizabethans rejected laziest' is the wordplay.
'rejected' indicates named letters should be taken away.
'elizabethans' with 'laziest' taken away is 'BEHAN'.
(Other definitions for behan that I've seen before include "Brendan - - , playwright" , "Brendan - - (Irish lit.)" , "Brendan...wrote ''The Quare Fella'' (5)" , "Brendan --, Irish author" , "Brendan . . . . . , author of ' 'Borstal Boy' '" .)