Another possibility is a story where the magic in the Harry Potter universe has a connection to the spiritual energy in the Bleach universe (where Arrancar and Ichigo are from). A powerful spell goes wrong and starts to merge the two worlds. Ichigo has to adapt to the new magical rules while dealing with the Arrancar who are also trying to take advantage of the situation. Harry Potter, on the other hand, is intrigued by Ichigo's abilities and they work together to fix the spell.
One idea could be a crossover where Ichigo, with his Soul Reaper powers, is somehow transported to the Harry Potter universe. He meets some of the Arrancar there who have also found their way into this new world. They could be causing chaos, and Ichigo teams up with Harry Potter and his friends to stop them. Maybe the Arrancar are attracted to the magic in the Harry Potter world and want to harness it for their own power.
A more serious fanfic could be set in a post - apocalyptic world that was destroyed by a combined force of villains from both Naruto and Bleach universes. Naruto and Ichigo are the last hopes. They meet and initially clash due to their different ways of fighting and beliefs. But they gradually learn from each other and combine their powers in a unique way to take on the remaining villains and try to restore their worlds.
One idea could be a story where a Wendigo somehow enters the wizarding world of Harry Potter. Maybe it's brought in by a dark wizard who wants to use it as a weapon. The Trio - Harry, Ron, and Hermione - would then have to figure out how to defeat it using their magic and knowledge.
One idea could be that Hulk somehow gets transported into the wizarding world of Harry Potter. Maybe a magical experiment gone wrong by a Hogwarts student creates a portal that sucks Hulk in. He could then cause chaos as he's not used to the magic and strange creatures there.
If we consider an encounter between them in a fanfic, Ichigo would likely be very cautious around the Arrancar at first. He has fought them before in his own world and knows their power. In the presence of Harry Potter and his friends, Ichigo would be curious about their magic. Harry, in turn, would be amazed by Ichigo's sword and his ability to fight spirits. The Arrancar might view the wizards as a new source of power or a threat, depending on their motives. For example, an Arrancar might try to steal a wizard's magic for themselves.
Another concept is that the magic from the Harry Potter series starts to seep into the DC universe where the Justice League operates. This causes chaos as the laws of physics in the DC world are disrupted. The Justice League has to seek help from Hogwarts professors to understand and contain this new form of magic energy. Superman might be intrigued by the idea of magic being a new power source or a new threat he can't easily overcome with his super strength.
One idea could be that Tony Stark somehow discovers the wizarding world while working on a new technology. Maybe his sensors pick up some strange magical energy. He then meets Harry Potter and they team up to face a new threat that combines magic and technology, like a dark wizard using Stark Industries' tech for evil purposes.
One idea could be a fanfic where Harry Potter discovers a hidden portal in Hogwarts that leads him to the time of King Arthur. He could use his magic skills to assist Arthur in battles, perhaps using spells to defeat the enemies that Arthur's knights struggle with. For example, Harry could use the Stunning Spell to incapacitate a large group of invaders.
One idea could be to have nanomachines in the Harry Potter universe that are secretly created by a dark wizard. They could be used to control the minds of students, but the protagonists discover this and use magic inspired by LotR spells to combat it. For example, a Patronus charm with a LotR - like incantation to repel the nanomachine - influenced dark magic.
A third fanfic concept could involve a character from the Harry Potter series stumbling into Alma Wade's world. Let's say Hermione accidentally discovers a portal that leads to Alma's realm. She has to use her knowledge of magic and her wits to survive in this strange new place. Meanwhile, Alma Wade is intrigued by Hermione's magic and they start to learn from each other, with Hermione introducing wizarding spells and Alma sharing her unique powers.
One idea could be to have the wizards from Harry Potter's world discover the Stargate Atlantis technology. Maybe they could use magic to help repair or understand some of the advanced technology in Atlantis. For example, Hermione could use her vast knowledge of spells and ancient runes to decipher the Atlantis control panels.