I read Pierce's The Immortals back in middle school and remember only fragments today, so I came into Tempests and Slaughter with very little to go on. I didn't even remember who Numair was.
Bearing that in mind, the book works well as a standalone coming-of-age fantasy, if a very accelerated one. Years go by in very few chapters. We have three friends: Arram Draper, our hero the future Numair, Varice, clever and beautiful, and Ozorne, a member of the imperial family. The three of them have such strong talents that they are separated from the bulk of students and have mostly private classes with the masters. Arram's schedules are included periodically to signal time passing and to give a sense of what he is studying.
This isolation from the other students except for a convenient plot bully or three made it very difficult to get a sense of the setting. I realize there are twenty-odd Tortall books so Pierce may not feel the need for much exposition, but I felt a little left out and bewildered as we see our three protagonists march forward effortlessly through their studies.
By the end of the book, the first of a trilogy, we have a sense of Arram's priorities and we get clues of Ozorne's true character. Conflicts of later books such as divine interference, the immortals, and imperial aggression and slavery are also touched on.
For established fans, there is a lot to love here. I'm just not sure that this would be rewarding to a new reader.