To start The Lost Astrolabe side quest in Hogwarts Legacy, travel to Lower Hogsfield, which is south of Hogwarts. You’ll then want to head over to the dock and speak with Grace Pinch-Smedley. She’ll ask you to retrieve an astrolabe belonging to her late grandparents from the bottom of the lake.
To do this, you’ll need to swim out northeast of the dock until you reach the purple circle on the mini-map. There will be several air bubbles here where you can dive. Make sure to dive at all 5 of the locations to get some good loot along with the quest item.
Return to Grace on the dock the speak with her to hand over the astrolabe. You have several options when speaking with her. You can simply hand it over, demand compensation or choose to keep it for yourself. No matter your choice, you’ll receive a Mermaid Mask appearance. If you demanded compensation, she’ll think that is fair and you’ll receive an additional 20 gold.