Poet’s dwelling on river (5)
I believe the answer is:
homer
'poet's' is the definition.
(Homer is an example)
'dwelling on river' is the wordplay.
'dwelling' becomes 'home' (synonyms).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'river' becomes 'r' (abbreviation).
'home'+'r'='HOMER'
(Other definitions for homer that I've seen before include "Ancient Greek author" , "Pigeon; classic writer" , "Old Greek epic poet" , "addition to the score?" , "Measure < of poet's" .)