Greek character was first to turn up with word of gratitude (5)
I believe the answer is:
delta
'greek character' is the definition.
(letter from the Greek alphabet)
'was first to turn up with word of gratitude' is the wordplay.
'was first' becomes 'led' (to lead is to go first).
'to turn up' says the letters should be written backwards.
'with' is a charade indicator (letters next to each other).
'word of gratitude' becomes 'ta'.
'led' backwards is 'del'.
'del'+'ta'='DELTA'
(Other definitions for delta that I've seen before include "Area of distributaries in a river basin" , "Comms code for 'd'" , "Triangular river system" , "Wide silted river mouth" , "Divided river outlet" .)