Major newspaper owned by the state (8)
I believe the answer is:
national
I believe this is a double definition.
'major newspaper' is the first definition.
(a newspaper published nationally)
'owned by the state' is the second definition.
(owned or run by the nation)
(Other definitions for national that I've seen before include "Generally respected senior public figure?" , "State-owned" , "Citizen of a particular country" , "Countrywide" , "57-year-old carer needing care?" .)