The foundation of this sense of danger must be an existential threat, a looming disaster, confronting the player. This can be achieved by implementing 3 changes to the grand campaign as found in Attila, the most current Total War: making the AI more aggressive, giving more meaning to alliances, and eliminating the sacking/razing mechanic.
I recently started playing Shogun 2 again on my channel as a part of my "Legacies of Total War" series. I was absolutely amazed by it. Going back to it from Attila, I immediately noticed how much more fun I was having. Don't get me wrong: I don't hate Attila, nor do I think it's necessarily a bad game. It's just that Shogun 2 is so much better. I would go so far as to say that it is, in fact, the best Total War game ever designed. That doesn't necessarily mean it's everyone's favorite Total War game, but it is fantastically well made.