。
Cold War tensions ran high.
Literal
Cold-War [of-の] tension [subject-が] rose-high.
高まる is an intransitive change-of-state verb: 'to rise, intensify, become stronger.' Its transitive counterpart is 高める ('to raise, elevate'). 緊張 ('tension, strain') is a noun often paired with 高まる to describe rising stakes.