The Silver State, capital Carson City (6)
I believe the answer is:
nevada
I believe this clue is a double definition.
'the silver state' is the first definition.
(synonyms)
'capital carson city' is the second definition.
(I know that Nevada has the capital city Carson City)
(Other definitions for nevada that I've seen before include "Arid US state" , "Sagebrush State" , "South-west US state" , "US state, capital Carson City" , "State including Las Vegas" .)