The last supporter may finish poem (5)
I believe the answer is:
elegy
'poem' is the definition.
(elegy is a kind of poem)
'the last supporter may finish' is the wordplay.
'the last' becomes 'e' (I've seen this in other clues).
'supporter' becomes 'leg'.
'finish' indicates one should take the final letters.
The final letter of 'may' is 'y'.
'e'+'leg'+'y'='ELEGY'
(Other definitions for elegy that I've seen before include "Requiem" , "lines of regret" , "A sorrowful poem - Gray wrote a famous one" , "Sad work" , "Mournful work" .)