Hit an alien, given new order to destroy (10)
I believe the answer is:
annihilate
'destroy' is the definition.
(thesaurus)
'hit an alien given new order' is the wordplay.
'given' is a charade indicator (letters next to each other).
'new order' is an anagram indicator.
'hit'+'an'+'alien'='hitanalien'
'hitanalien' anagrammed gives 'ANNIHILATE'.
'to' acts as a link.
(Other definitions for annihilate that I've seen before include "Utterly destroy" , "Completely defeat" , "Wipe out" .)