Story, finish first stage (6)
I believe the answer is:
legend
'story' is the definition.
(legend is a kind of story)
'finish first stage' is the wordplay.
'finish' becomes 'end' ('end' can be a synonym of 'finish').
'first' is a charade indicator (letters next to each other).
'stage' becomes 'leg' ('leg' can be a synonym of 'stage').
'end' after 'leg' is 'LEGEND'.
(Other definitions for legend that I've seen before include "Superstar" , "Inscription; myth" , "Story from long ago" , "Story of mythical beings or events" , "King Arthur" .)