Mystery writers' award (5)
I believe the answer is:
'mystery writer's award' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for edgar that I've seen before include "Fellow" , "10th-century king" , ". . . . . Allan Poe, master of the macabre" , "Great writer of spooky stories, . . . . . Allan Poe" , "Chap" .)