Writer's wife managed deli (5)
I believe the answer is:
wilde
'writer's' is the definition.
(I've seen this before)
'wife managed deli' is the wordplay.
'wife' becomes 'w' ().
'managed' indicates anagramming the letters.
'deli' anagrammed gives 'ilde'.
'w'+'ilde'='WILDE'
(Other definitions for wilde that I've seen before include "Oscar --, writer and wit" , "Oscar --, playwright, wit and author" , "Oscar -, Irish author" , "Author of The Portrait of Dorian Gray" , "Irish dramatist and wit" .)