The first step is to find the NPC that will teach you the gesture. Thops is an ex-Academy student who can be found in the Church of Irith, located to the very south of the remodeled Fringe Tower itself. Thops will give you his side quest if you ask him for the Academy Glintstone key. The quest requires you to have gotten past the Radagon Red Wolf and gained access to the Debate Parlor Site of Grace. Using this as a starting point, you then have to walk across the rooftops to get the key from the Cuckoo Church chandeliers.
Once you give Thops the key and learn the Scholarship gesture, you need to find a Glintstone Crown. Note, however, that only the five crowns that can be found in the Academy itself are suitable for solving the puzzle: the crowns of Lazuli, Twinsage, Karolos, Olivinus, and Witch Glintstone. If you’ve done your thorough research so far, you most likely already have one of these; If not, the Karolos Crown can be looted by a Crystalized Crab a short run from the Debate Room (according to Gamer Guru).
After that, all you have to do is equip the crown and perform the gesture in front of the locked door on the tower. there is another enemy behind the door so be careful and enjoy your new spells.