In order to begin The Lost Astrolabe in Hogwarts Legacy, you need to travel to Lower Hogsfield, where you meet up with Natty to discuss what happened to you before your sorting ceremony and why you were late. Once you’ve made it there, look around until you find that student that is standing on the dock over the Black Lake. This is Grace Pinch-Smedley. Go speak with her to begin your Side Quest.
Once you’re out in the lake, it shouldn’t take long for you to notice that something is very clearly off about the water. Every so often throughout the highlighted portion of your minimap, you will see spots in the water that look like the one pictured above. Though, there are only 4 or 5 of them, you should swim up to each of them and search for them. While only one of these spots with contain the Lost Astrolabe, the others will contain pieces of gear in varying rarities. Search through every spots you can find in the area and head back to shore.
After you’ve collected the Astrolabe, swim to shore and hop back up onto the Dock where Grace is waiting for you. Return the Lost Astrolabe to her and collect your reward of 180 XP.