Carpathian is going to resolve hostility (3,4)
I believe the answer is:
ill will
'hostility' is the definition.
(synonyms)
'carpathian is going to resolve' is the wordplay.
'carpathian' becomes 'I' (where the crossword setter is 'Carpathian').
'is going to' becomes 'll' (as in he'll, we'll etc).
'resolve' becomes 'will' (I've seen this before).
'i'+'ll'+'will'='ILL-WILL'
(Other definitions for ill will that I've seen before include "Malice - unfriendliness" , "Hostile and unkind feeling" , "Animosity, hostile feeling" , "causing resentment" , "Rancour" .)