Writer having a set back (5)
I believe the answer is:
aesop
'writer' is the definition.
(I've seen this before)
'a set back' is the wordplay.
'set' becomes 'pose' (synonyms).
'back' says the letters should be written in reverse.
'pose' in reverse letter order is 'esop'.
'a'+'esop'='AESOP'
'having' is the link.
(Other definitions for aesop that I've seen before include "Ancient Greek fabulist" , "story teller" , "Greek storyteller" , "Greek fabulist (Tortoise and the Hare)" , "Greek author, famous for his fables" .)