I'd say:
You need to plot each book individually, but at the same time you need to plot the whole series. For example, while each book needs to have its own climactic crisis and satisfying solution, the mother of all climaxes and the final solution to everything needs to happen in the last volume.
If you think of the plot as a series of summits with increasing height, you can understand each book as one such "mountain of tension and relief". But the mountains still sit on one single mountain range, and it is this connection over an underlying structure that makes the volumes part of a series-with-an-end (such as a trilogy) instead of random instances in an endless series (such as most superhero comic books that you can read in any order).
The same goes for character arc. So what you need to do is think about the development of your protagonist's magical ability as happening over the course of the whole series. If the ability first shows itself in the second volume, you still need to build up for that in the first: the mountain range has to be there, and if there is a summit in the second volume, there needs to be a lower summit in the first.
Fiction is not reality. It is completely normal and happens quite often that people brush their teeth. In fiction you don't have your protagonists brush their teeth after every meal.
So while it might be totally realistic that a person discovers an ability that they had known nothing about, in fiction something must lead up to that discovery or it will appear random. If there are no dragons in the first volume of your books, they cannot simply appear in the second. Authors do that, of course, but it is bad manners.
So think how your protagonist's magic makes sense in the overall plot. Maybe she is laughed at for not having magic in the first volume and feels ashamed. That can be a short one paraghraph scene, but will lend credibility to her finding she has it and feeling relief in the second volume. Or you can have her think about how nice it would be to have magic, only to realize in volume two that it takes specific circumstances that were not present until then.
Create something in volume one that does not give away the future, but that readers can remember and will serve as continuity for them.
Hope that helps.