Well, he might use his magic to defeat the dragons in Skyrim. Maybe he'd introduce some new spells to the mages there. It could be really interesting to see how his Hogwarts-trained skills fare against the challenges of Skyrim.
His other friends from Hogwarts might not even believe it at first. They might think it's some kind of elaborate prank. But once they realized it was real, they might try to find a magical way to communicate with him in Skyrim, or even try to open a portal to bring him back.
The main antagonist could be a powerful necromancer who combines the dark arts of Skyrim with some elements of Voldemort - like magic. He could be raising an army of the undead and causing chaos across Skyrim, which Harry has to stop.
One interesting concept could be the combination of magic systems. In Harry Potter, there's wand - based magic, while Skyrim has shouts and spellcasting in a different way. A fanfic might explore how wizards from Hogwarts would adapt to the magic in Skyrim, or vice versa. For example, a Hogwarts student trying to master a dragon shout.
One idea could be Harry Potter arriving in Skyrim and using his magic to combat the dragons. Maybe he teams up with the local mages and they learn from each other's magical techniques.
Research is key. The writer needs to be well - versed in both the Harry Potter universe and Skyrim. Know the rules of magic, the cultures, and the lore of both. For instance, understanding how Patronuses work in Harry Potter and the significance of the different races in Skyrim.
The common folk in Skyrim would probably be a bit scared at first. Harry's strange clothes and the fact that he can do magic so effortlessly would be quite intimidating. But if he helps them out, like getting rid of a bandit problem or curing a disease, they would soon start to accept and even revere him as a powerful hero.
Well, the plot could involve Harry using his magic skills in the world of Skyrim. Maybe he's hired to protect a powerful mage in Skyrim from the various threats like dragons or bandits. He'd have to adapt his Hogwarts - learned magic to the different magical rules of Skyrim.
He might meet the house - elves that have been taking care of Potter Manor for generations. They could show him around the manor and tell him stories about his family.