The History of Magic Class side quest in Hogwarts Legacy becomes available during the Prepare for Your O.W.L.S main objective. Travel to the Bell Tower Courtyard Floo Flame then head up the stairs on the southwest side and through the door straight ahead. Go up the stairs and into the History of Magic class the being the quest. You’ll have to follow Professor Binns through the school on a guided field trip. You’ll then have to collect the Grimbald Weft Field Guide Page. It can be found next to right of the Floo Flame (when looking at it) in the nook of the stairs. Use Revelio to make it appear and collect it.
Next, you’ll be tasked with locating the Waving Knight Guide Page. It can also be collected by using Revelio on the stone statue in the wall to the left of the Floo Flame (when looking at it) at the top of the second flight of stairs.
Speak with the professor afterward. This will complete the quest and you’ll be rewarded with a Books and Cauldrons Shelf conjuration.