A cutscene will play, where Natsai and you will split up going in separate directions. To continue the climb, go around to the left and scale that wooden structure. Continue climbing up. The way is fairly straightforward from here, with diversions for treasure rooms, including a room where several Beasts can be rescued in Hogwarts Legacy. Around the corner is a crate to levitate to climb the next wall. After that, there will be several groups of poacher enemies, so keep combat spells at the ready. There is an Alohomora puzzle to get into the keep nearby, behind which there will be a double staircase going up.