In the beginning of the 21st century, a world war breaks out over interplanetary travel tech. The environment is pretty much destroyed so mankind leaves Earth, settling on other planets, and starts Star Calendar 00.
Entertainment and songs become heavily regulated and eventually banned on several planets due to their power to move people, but a brave idol group puts on guerrilla performances in these systems in the name of a famous act from earlier times that sang to Earth's bitter end, AKB48. Famous throughout the galaxy, the group's name is AKB0048.
This story centers around a group of girls from various planets, some where entertainment is banned and some, where it is not, striving to become great idols and join AKB0048.
Therefore, they participate in the entrance exam and eventually become undergraduates, aiming to someday succeed the current members of the group.
(Source: Crunchyroll, edited)