Society dramatist of Elizabethan times in the manner of Fox (5)
I believe the answer is:
slyly
'in the manner of fox' is the definition.
(foxes are said to be sly)
'society dramatist of elizabethan times' is the wordplay.
'society' becomes 's' (common abbreviation in names of organisations).
'dramatist of elizabethan times' becomes 'Lyly' (John Lyly, 1553-1606).
's'+'lyly'='SLYLY'
(Other definitions for slyly that I've seen before include "in underhand way" , "Craftily, cunningly" , "In a stealthy and secret way" , "In a cunning manner" .)