Each new book should have enough information to understand the new book without being overwhelming and sounding like an info dump.
Select the strict minimum and slowly trickle this information in. Often readers have to wait several years before they can read the next book, so meanwhile they have forgotten a lot.
EXAMPLE: It took 12 years between the publications of Jean Auel's The Plains of Passage and The Shelters of Stone. Asimov took decades to write the next book in the collection of the Foundation series.
You don’t want the reader to go back and read all the previous books, but you don’t want to rehash info from previous books either.
EXAMPLE: In the second volume of Harry Potter, J.K. Rowling had to face the fact that some of the readers would not understand the game of Quidditch. But since Harry did not have to relearn the game, there was no way she was going to explain it again. She went around the problem by making Harry explain the rules of the game to a new student.
Be clever about the info you re-explain, and make sure you do not forget to build suspense, introduce new characters, and introduce the reader to new aspects of the world in the first 25% of each new book.
Each book should have its own arc and have a good resolution. In other words, book 2 is not the resolution for book 1. One way to do that is to get rid of the villain’s sidekick. In Harry Potter, the death Eaters are expandable.
The more sub-text there is, the more your plot will be successful. The sub-text, up to David Baboulene, is the story that is not written down, it’s the underlying story that develops in the back. “It’s any sort of knowledge gap” that will intrigue the reader, any lie that is hinted at or the shadow of a deceit.
Create linked titles so that the reader can easily figure out they are books from the same series.
Examples are Harry Potter and The deathly Hollows/Harry Potter and The Sorcerer’s Stone, etc. City or Bones/City of Ashes/City of Glass. Clockwork Angel/City of Fallen Angels/Clockwork Prince. Uglies/Pretties/Specials. Waterfall/Cascade/Torrent.
Include some unfinished businesses and conclude unfinished businesses to add more depth to the story and create a feeling of expectation.
In each new book, the world you have created should be different because your heroes have changed and their point of view has changed too. They do not see their world with the same eyes. It makes sense to treat the familiar characters like new characters and show how they have evolved from the previous book. Do they have nightmares now? Do they walk more confidently? Are they more introspect and less social? Use the characters to make the change obvious. Someone could ask your protagonist why they don’t carry an umbrella everywhere anymore. That’s because the protagonist has been electrocuted in the past through his umbrella, so he dropped the habit. In book 2 of The Hunger Games, Katniss lives in a mansion as opposed to book 1. She is rich and famous, but spied on and needs to keep the appearance of a fake romance going.
Penn, Joanna. "Improving You Story With David Baboulene."