Conclusively (4,3,3,3)
I believe the answer is:
once and for all
'conclusively' is the definition.
(synonyms)
This is all the clue.
(Other definitions for once and for all that I've seen before include "Finally" , "For the last time" , "how might an inclusively unique show be performed?" , "unique public statement?" , "In a conclusive way" .)