If you're lucky enough to have a book published, two questions arise: will you write a sequel and if so, how should you go about it?
The first question is fairly easy to answer. Most of us know that publishers like series, and if you have a decent idea, you probably should start on the sequel the day after you sign that contract, even if you have a hangover from the celebration.
But how do you segue from the original story, which publishers usually want to be able to stand on its own, to another one, related but not repeated? How much of the first story do you have to tell as events unfold in the second?
That isn't easy. Having read series out of order and been confused by them, I think it's essential for an author to be clear about who is whom. However, those who read the first book know who is whom, and they want to get on with the new story. So what is the balancing point?
It can be done, mostly by alluding to past events casually but briefly. A new reader doesn't need to know WHY your protagonist moved to England in the last book, just that she did. Comments made by characters in the book can clarify who she is and give details that are important about her previous adventures. What I (and many others) dislike is when we get a long synopsis of the first book's events told as exposition at the beginning of the second. It tends to be pedantic and un-storylike, pulling the reader away from where she wants to be, inside this book.
Still, there are things that have to be told. Why have these two sisters not seen each other for ten years? There are things that repeat simply because they have to: both sisters had the same mother, the same father, and some mention must be made of their personality traits. And of course characters repeat: family friends, servants, and even bad guys may return in a sequel. The trick is to make references clean and to the point. It helps if there are differing perspectives: maybe the main character in Book 1 is a secondary character in Book 2. If not, certainly the character is at a different stage of life: she has grown up or grown old or grown in some other way.
Changing perspective, altered focus, comments in dialogue all can give a sequel the fresh approach it needs while allowing the storyteller to reacquaint previous readers and inform new readers. Readers love meeting old friends again in books. They just don't want them to become too repetitive.