The gutted North American town shows resolve (8)
I believe the answer is:
tenacity
'resolve' is the definition.
(tenacity is a kind of resolve)
'the gutted north american town' is the wordplay.
'gutted' suggests removing the centre (to gut something is to remove its insides).
'north american' becomes 'na'.
'town' becomes 'city' (I've seen this in other clues).
'the' with its centre removed is 'te'.
'te'+'na'+'city'='TENACITY'
'shows' acts as a link.
(Other definitions for tenacity that I've seen before include "Stubbornness, determination" , "Dogged resolve" , "Perseverance, doggedness" , "Perseverance in chosen course" , "Ability to stick firmly to task or position" .)