Resolve to check explosive device (9)
I believe the answer is:
determine
'resolve' is the definition.
(determining is a kind of resolving)
'check explosive device' is the wordplay.
'check' becomes 'deter' (I've seen this in other clues).
'explosive device' becomes 'mine' (mine is a kind of explosive device).
'deter'+'mine'='DETERMINE'
'to' is the link.
(Other definitions for determine that I've seen before include "Establish" , "Decide - to settle" , "resolve" , "Discover" , "Ascertain by research or calculation" .)