Complex sentence: Fearing that the Soviets would overrun the country, Kállay, with Horthy's approval, put out numerous feelers to the Western Allies, promising to surrender unconditionally to them once they reached Hungarian territory.
Split into simpler sentences: Fearing that the Soviets would overrun the country, Kállay, with Horthy's approval, put out numerous feelers to the Western Allies. He even promised to surrender unconditionally to them once they reached Hungarian territory.