Destroy ancient EU state (9)
I believe the answer is:
enunciate
'state' is the definition.
(enunciating is a kind of stating)
'destroy ancient eu' is the wordplay.
'destroy' indicates an anagram (I've seen this in other clues).
'ancient'+'eu'='ancienteu'
'ancienteu' with letters rearranged gives 'ENUNCIATE'.
(Other definitions for enunciate that I've seen before include "Speak with precision" , "State clearly or formally" , "giving voice" , "State clearly like cute Annie" , "Articulate" .)