As for the story of the war and some of the characters stories... The age of heroes like Kirk in their prime is over, the federation is losing the war. Younger crews weren't properly mentored and so lack the knowledge of the aging heroes and so are not doing well at all, and the older crews dont have the vigor to engage in total war. Meanwhile the Klingons seem to be doing just fine, being both vigorous and wise, hence why they decided to start a war sensing a weak federation. Kirk would slowly over the course of the movie learn that it's not so bad mentoring top people. Bones would struggle after watching the young men come into the sickbay dead realizing in just a few years his final destination would be upon him, and he'd be making mistakes and cracking. Spock would share his struggles with his grandfather dying and would speak logically about death like nimoy did in "I am Spock" and it would help McCoy put death into perspective. Scott would learn he drank because he didn't think he had anything better in his life until he saw the new batch of engineers trying really hard to keep the ship running but lacking know-how and one of the engineers would come to him with personal problems and he'd realize he had more to offer than just work. Spock would do some brilliant work as a seconded science officer and later would use his skills as a diplomat to help end the war with the Klingons once the Enterprise becomes the focal point of a passing of the torch where the old crews realize they need to build up the new ones which makes the Klingons realize their time has passed to attack (with a little prodding). Uhuras work as a communications officer ends up front and center as she is a second diplomat working with Spock near the end of the movie. Checkov would realize that while he isn't happy with his past all he can do is move on to his future. Sulu would have a whole b-plot where he talks at desks about strategy and helps see several ambushes by the Klingons in advance which is part of what helps end the war.

Ok but that's it...