Maybe Harry leaves England to explore the wizarding world in other countries. He could go to France to study different magic spells at Beauxbatons Academy. Or perhaps he travels to America to help the MACUSA (Magical Congress of the United States of America) deal with some dark magic threats.
One possible plot could be that Harry Potter discovers he is pregnant (through some magical means perhaps) and decides to leave England because he wants to protect his unborn child from the dark forces that still lurk in the country. He might go to a far - off magical land where he can raise the child in peace and secrecy.
He could meet new witches and wizards from different cultures. For example, he might run into a powerful African wizard who has unique magical abilities related to nature magic. Or he could meet a Japanese witch who specializes in charm - making that is based on ancient Shinto beliefs.
Perhaps it's a completely new character, a powerful and mysterious wizard who came into Harry's life. Their encounter led to Harry's pregnancy, and the fear of this unknown wizard's intentions and the reaction of the English wizarding community makes Harry leave England.
One possible plot could be that Harry discovers he has some long - lost royal blood. He then has to navigate both the wizarding world and the political intrigues of the English court as he tries to balance his newfound status as a potential king. Magic could be used to solve problems within the monarchy, like protecting the king from dark magic threats.
One possible plot could be that Harry Potter discovers his secret heritage as a Prince of England. This might lead to a whole new set of magical and political adventures. He could use his newfound status to reform the wizarding world's relationship with the Muggle government. Maybe he'd introduce magical solutions to some of the Muggle world's problems, all while still dealing with the usual threats in the wizarding world like Voldemort's followers.
Well, it could be about the Queen of England being a secret witch and having a connection to the wizarding world of Harry Potter. Maybe she helps Hogwarts in some way during a crisis, like providing a safe haven on the castle grounds that are protected by magic and Muggle secrecy charms at the same time.
One possible reason could be to protect Teddy. Maybe there are some threats in England that Harry wants to keep Teddy away from. For example, there could be some dark wizards or dangerous magical creatures that target Teddy for some reason.
One possible plot could be that the Queen of England discovers the wizarding world through Harry Potter. Maybe she visits Hogwarts and is amazed by the magic there. She could then use her influence in the Muggle world to help keep the wizard - Muggle relations a secret in a more official way.
Maybe Harry Potter is wrongly accused of a great crime in the wizarding world of England. The Ministry of Magic, fearing his power or influenced by dark forces in disguise, decides to banish him. He then has to start a new life in other parts of the magical world, perhaps in France or America, facing new challenges and making new friends along the way.
A great 'Harry Potter Leaves England' fanfic should have a strong reason for Harry to leave. For example, if he's leaving to escape the trauma of the war or the overbearing attention. It also needs to have an interesting destination. If he goes to a place like Egypt with its rich magical history, it can add a lot to the story. Good character development is crucial too. We should see Harry evolving as he experiences new things in a different place.