Tomes and Tribulations is a main story quest in Hogwarts Legacy.
Your objective is to simply give him the book you found in the restricted section of the library.
Here’s a walkthrough and guide of Tomes and Tribulations in Hogwarts Legacy.
The required level is 3.
Meet with Professor Fig
To find Professor Fig, head to his classroom. Use the compass to get there.
Go to the marked spot and wait for him to arrive.
Enter his room and you’ll see that he’s having a conversation with Professor Black on the issue of Ranrok and Rookwood collaborating.
Talk to Professor Fig about the book you found. He’ll say that he goes to London to meet the minister.
The quest ends here.