As you may already know, the Fire Emblem Three Houses Expansion Pack, Cindered Shadows, presents itself as a secondary story centered on the Abyss, far below the monastery.
The progression of the story will follow a different cycle from the calendar, and you will not have access to the majority of the activities. Giving lessons to students to improve their mastery and unlock classes will not be possible, even if all the details are not yet known.
New official information has made it possible to find out a little more about this. All of your characters will have several classes already unlocked, and you will be able to select the one you want before the battle, depending on your needs. New classes should also be made available as you progress through the story.
It's the same for Abilities: each character has a range of bonuses already unlocked, and all you have to do is activate the ones you want to use.
There are not only students from the House of Ashen Wolves in the 4th DLC of Fire Emblem Three Houses. There is at least one new teacher from the church of Seiros, representing the officers' academy in the Abyss.