Old Greek writer's place, penning line, by bridge (8)
I believe the answer is:
plutarch
'old greek writer's' is the definition.
(Plutarch was a Greek writer)
'place penning line by bridge' is the wordplay.
'place' becomes 'put' (synonyms).
'penning' indicates putting letters inside.
'line' becomes 'l' (used when specifying particular lines from a poem).
'by' is a charade indicator (letters next to each other).
'bridge' becomes 'arch' (I've seen this before).
'put' enclosing 'l' is 'plut'.
'plut'+'arch'='PLUTARCH'
(Other definitions for plutarch that I've seen before include "old biographer" , "Classic Greek biographer" , "classical biographer" , "Greek writer" , "Classical Greek essayist (Parallel Lives)" .)