When you write a book that’s part of a larger arc of conflict, you want to end in a way that creates closure, but also spurs the reader on to the next book. A cliffhanger can certainly do this, but that approach can also feel heavy-handed, particularly if the cliffhanger’s only role is to get you to the next book.
Instead, you might think of how each book functions as an individual entity, in addition to its role in the larger story line. To that end, create meaningful closure for each individual book. Bring resolution—in whatever form that takes—to the main thrust of conflict in that particular book, so the reader feels they have come to an end. At the same time, leave compelling questions that encourage the reader to the next book. These questions might have to do with an aspect of the main conflict that was resolved, or they might emphasize a strain of conflict or a question that runs though the book but is not yet resolved. Your negotiation of these questions will influence whether the reader feels mild intrigue or significant urgency to get started on the next book.
Individual books in trilogies—or larger works—need to function on their own while, at the same time, contributing to the larger story. It’s a duality that complicates the author’s choices, but strengthens the reading experience for the reader of an individual book and the reader of the whole series.