I believe China will play an increasingly active role.
Literal
China [subject-が] more active role [object-を] demonstrate-going [thing-ものと] believe.
Formal diplomatic or editorial language. ~ていく on 発揮する (demonstrate/exercise) points the action into the future. ~ものと信じる is a formal construction: 'I believe that X will (come to pass).' より積極的な (more active) uses より as a comparative adverb.