Hogwarts Academy of Magic
When Harry Potter first enters this prestigous school of learning, the first major difference one might notice is the Great Hall. It is much bigger than in canon. There are no four benches for the houses. Instead there are many round tables with seats for four students each, with each table styled differently, and a set of tables that are currently plain wood and blank with no one seated at them.
The upper years watch as the first years come into the hall, marvelling at the floating candles and the ceiling enchanted to look like the sky outside, and are lined up all next to each other. One by one each are called up and have the sorting hat placed on their head. After a time the sorting hat calls out next and the child goes back to the group.
Once the sorting hat has called and sat upon the heads of each child, it deliberates for a few moments, then begins to call up students in groups of four. The sorting hat assigns them a table, a team name, and a dorm room, by which magic creates for them as needed in one of the seven towers of Hogwarts, one for each year, with the first years taking the tower the previous seventh years graduated from.
Harry is sorted into a group consisting of two girls and two boys. One of which is him, the others are his partner, Pyrrha Nikos, and Lie Ren partner of Nora Valkerie. Their sister team across the hall from their dorm is Juane Arc partnered with Hermione Granger with Neville Longbottom partnered with Ruby Rose. (Weiss Schnee is in another dorm partnered with Draco Malfoy, while Yang and Blake are in a second year dorm)
The next major difference one might see is that while the normal Hogwarts classic curriculum are still scattered throughout the week on various days as usual, though History of Magic is conspicuously missing, every day of school barring weekends there are four core classes taught every day during one of seven time slots for each year group at Hogwarts. They are taught by the ghosts of the four founders.
The first is a combat class lead by Salazar Slytherin, where mages are taught to hone their battle aura, the first manifestation of magic, to protect them and hone their skills in fighting one on one, two on two, partners vs partners, or four on four, teams vs teams.
The second is an aura manifestation class, taught by Helga Hufflepuff, where unique skills to each mage are discovered and honed, as well as learning to manifest the weapon of your soul, in whatever form it may be (Gryfindor will be tickled pink when Harry ends up manifesting his own sword and shield, allowing the Sword of Gryffindor, Crocea Mors and its companion shield to ride out into battle once again)
The third is World History and Battle Tactics taught by Rowena Ravenclaw, which covers history, geography, and the study of past battles and their effects on history and what sorts of tactics were used and how/why they were effective or ineffective.
The fourth class is Enemy Studies taught by Godric Gryfindor. In which each type of enemy that a mage may face or has been faced in the past is discussed, further expanding on the Battle Tactics aspect of class, along with potential forays into enemy territory for teams with teacher oversight/supervision in case the team needs bailing out of a situation. These forays happen on the weekends in various time slots, with teams selected by one of the teachers.
There is an extra class replacing the defunct history of magic class from the original hogwarts curriculum since World History with Rowena replaces it. Healing Arts taught by Poppy Pomphrey, a class that often gets interupted/added to as it's an informal class where the younger years are taught either directly by Pomphrey or by watching medical theater style as she heals up patients brought into her class. Upper years have the chance of actually getting involved in the healing process depending on their grades and Pomphrey's discretion.
As for the enemy that this world faces, it is not the Grimm. Hogwarts mages do not study to defeat the Grimm, though their enemy is just as dangerous, if not more so.
They fight Hollows. Creatures far more varied than Grimm, as numerous as Grimm, and able to appear anywhere in the world at a moments notice from their realm Hueco Mundo. Sixth and seventh year teams are on call at any moment to apparate to any location within range of Scotland, which includes Britain and the various isles, or portkey to support their sister academies of Durmstrang of Bulgaria or Beauxbatons of France, each of which handle the areas of Eastern and western europe respectively while Hogwarts handles the north. (there is also a shinigami academy in Japan that serves much the same purpose but is somehow even more traditional and old style than Hogwarts is)
Apart from Hollows of course, there are various other enemies that mages have had to fight that are more local, though by this age those enemies are mostly no longer a problem, as dragons and goblins have both more or less been brought under control more or less. (Goblins being less in that regard, but it's hard to oust an enemy that has a fortress in the middle of your shopping district that once belonged to the dwarves before the Goblins nearly drove them extinct, at least in the greater European area)
Meanwhile in Hueco Mundo, various hidden factions are in a shadow war with each other and the greater part of the world.
The first is Salem, the oldest with the ability to control Hollows directly, and has history and is arch enemies with Ozpin, the headmaster of Beacon Academy in Canada.
The second is Voldemort, who has control of his own faction of mages, with his inner circle consisting of his own team, their sister team, and two others from the same year, and has poached and corrupted a number of mages for his own group. Not exactly allied to Hollows, but Hollows leave them alone thanks to Voldemorts control of one specific type of Hollow, Dementors.
The third and last is Aizen Sousuke, formerly of Shinigami Academy, who is something of a mix of mad scientist and mad schemer. His goal is to transcend mages and give them Hollow powers and vice versa, which he has been more or less successful in, and intends to go after the higher escholons of mages in order to claim the throne of Spirit King, said to confer great power on whomever takes the seat, based upon legends of the old Spirit King, who lived for millenia, is accredited with creating Hueco Mundo and banishing Hollows there so that they no longer roamed the Earth (They were much more like Grimm then and the basis for many stories of demons and monsters), and seemingly disappeared a thousand years ago.