It's 670 years in the future, 1200 before Taylor crashlands back to Earth. The Lawgiver has been assassinated and the ape/human civilization may erupt in civil war. The assassin turns out to be a mute girl named Chaika, who becomes a suicide bomber.
Apes pretty much rule the earth, though many humans live in the slum of "Skintown". As soon as the Lawgiver dies, the city's ruler, chimp Alaya, acts out and wants to drive out all the humans. And human Mayor Sullivan, who had been raised with Alaya by The Lawgiver, will do everything she can for human rights. Alaya releases Nix, an albino gorilla general, from prison to help "deal" with the perceived "human situation". And Sullivan gets the help of Brother Kale, a bald religious leader who worships a nuclear bomb. They go out to the nearby swamp and rendezvous with his cult members, who have brought a boat load of weapons. With these new weapons groups of humans manage to shoot down the Ape's airships, which patrol the city.
18 years earlier was the last big Ape/Human war, in which the last human city, Delphi, was attacked by the largest Ape army. Bako, a friend of Sullivan's, had lost his wife and son to the apes, then spent the next decade and a half in the Ape City of Mak raising his mute daughter. This daughter would grow up to be the one who assassinated The Lawgiver and begin this whole problem, which culminates with her blowing herself up as a suicide bomber.
Ape leader Alaya wants to further stir up the apes to squash the humans, so on Caesar Day she produces a third (and made-up) lawgiver scrolll, which says "Beware the Beast Man, for he is the Devil's pawn. Alone among God's primates, he kills for sport, or lust, or greed. Shun him. Drive him back into his jungle lair, for he is the harbinger of death" (just as Dr. Zaius had quoted this in the first Apes movie). Of course, all the apes believe this. She wants to drive all humans from her city. In the last panel of issue #7 we see how she intends to do this-- with armored tanks!
The "Classic" Planet of the Apes movies have always reflected the time-period in which they were made and this comic does the very same thing, reflecting our current "terrorist obsessed" society with plenty of words like "Terrorists" and "Insurgents" thrown about.
Best of all, this fits in with the continuity of the original series.