This writer's a Greek character, seen in retrospect as having some taste (5)
I believe the answer is:
umami
'some taste' is the definition.
(I've seen this before)
'this writer's a greek character seen in retrospect' is the wordplay.
'this writer's' becomes 'I'm' ('I am' referring to the writer of the clue).
'greek character' becomes 'mu' (letter from the Greek alphabet).
'seen in retrospect' is a reversal indicator (retro means 'back' in Latin).
'im'+'a'+'mu'='imamu'
'imamu' reversed gives 'UMAMI'.
'as having' is the link.
(Other definitions for umami that I've seen before include "Newly discovered taste" , "Savoury flavour" , "Savoury taste sensation produced by glutamates - I, a mum (anag)" , "Japanese word for pleasant savoury taste" , "meaty taste" .)