All Supreme Kais died except Eastern Supreme Kai. Why new ones were not chosen? Only Eastern Supreme Kai is left, why he does all the job? There's supposed to be 4 Supreme Kais and 1 Grand Kai
We know the answer to this in the Majin Buu Saga in Dragon Ball Z. While Shin lived in the sacred world of the Kai's, Bibidi(Note: Babidi's father), targetted them and wanted to kill them. So he unleashed Majin Buu(Note: Kid Buu, his actual form) on them who ended up killing the North and West Supreme Kai. Kid Buu apparently then absorbed the Southern Supreme Kai and ended up transforming into Super Buu.Finally, whle this monster went after Shin and the Grand Supreme Kai. The Grand Supreme Kai intervened and was absorbed, which turned Buu into the Fat Majin Buu(The playful Buu we see the first time Babidi summons Buu). Hence he spared Shin's life. Shin later caught Bibidi off guard and destroyed him while Buu was in a ball and later hid the ball under the surface of the Earth. Since all the 4 supreme Kai's had died, Shin became known as simply the Supreme Kai who lived along with his body guard Kibito in the world of the Kai's.
This clip shows the scene where Shin narrates the same.With regard to why new Supreme Kai's weren't picked, there isn't a definite explanation as to why. I believe this theory of  multiple Supreme Kai's has been retconned for the sake of simplicity. Here are a few reasons whyIn the Universe Survival Arc, we see only 1 Supreme Kai from every Universe and they are referred to as "Supreme Kai" and not "Grand Supreme Kai" .The first reason indeed isn't completely factual but if you look at the episode where Goku, Beerus and Whis go to the Sacred World of the Kai's in Universe 10, we see Gowasu with only his apprentice Zamasu. We don't see any other Supreme Kais. Also, it would make sense for Gowasu to train Zamasu to make him a Grand Supreme Kai. He was training to become a Supreme Kai. So if other Supreme Kais exist, they obviously could've trained him instead.Shin is considered to be the weakest and least experienced Supreme Kai compared to the Supreme Kais across the multiverse. It wouldn't make sense for them to recruit a few more Supreme Kais(More inexperienced than him, because if they were more experienced, they would end up becoming the Grand Supreme Kai.Going back to the Future Trunks Arc. Zamasu only tried to kill Gowasu(In the present timeline). There is no mention of him trying to kill other Supreme Kai's in the same universe.Finally the best reason why I think this theory has been completely retconned is based on Episode 55. In this Episode, Whis states that The "Kaioshin and Hakaishin(In Singular) are a set" when Goku asks was curious at to Beerus was concerned about ShinOf course, this argument is indeed debatable and the only one who could give a definite answer would be the writers themselves. However, based on the information we have. I think it is fair to assume that this theory has been retconned for simplicity reasons.