Minister’s contribution to coup — a story! (6)
I believe the answer is:
pastor
'minister's' is the definition.
(type of church minister)
'contribution to coup a story' is the wordplay.
'contribution to' says the answer is hidden in the clue.
'PASTOR' is hidden within 'coup a story'.
(Other definitions for pastor that I've seen before include "Old shepherd" , "Minister of religion" , "One with a flock (of people)" , "Padre perhaps" , "Flock's leader" .)