Maybe Harry leaves Earth because he's being chased by dark wizards who have somehow gained control over the planet. He decides to flee to find a place where he can regroup and learn new magic to fight back. So he travels to other planets in search of ancient knowledge and allies.
Well, one possibility could be that Harry discovers a magical portal that leads to another planet. He leaves Earth because he's on a quest to find a powerful magical artifact that is said to be hidden in a far - off galaxy. Once he leaves, he has to deal with all kinds of strange new creatures and different forms of magic.
One possibility could be that Harry Potter leaves Earth to explore other magical realms in the universe. Maybe he discovers a planet where magic is used in completely different ways than on Earth. He could encounter new magical creatures and make friends with beings who have powers he's never seen before.
Dumbledore could also play a role even if Harry has left Earth. Maybe his spirit or some form of his magic reaches out to Harry from afar, guiding him on his journey and providing him with cryptic advice to face the challenges in outer - space - related magic.
One possibility is that Harry discovers some dark secret about Severus that makes him feel he can no longer stay in the same place as him. For example, if he finds out Severus had a hand in some past event that endangered his friends. So he decides to leave to protect himself and those he cares about.
It could be that they leave to attend a special magical training that is only available in a very secluded place. They might have received an invitation from a very powerful and reclusive wizard. This training could enhance their magical abilities in ways that Hogwarts or Beauxbatons couldn't. They see this as an opportunity to become stronger and more self - reliant, so they leave together, excited for the new challenges and knowledge that awaits them.
The plot might start with Jacob being in a relationship or a strong friendship with Harry. But then, Bella enters the picture. Bella has some unique qualities that attract Jacob. As he gets to know Bella more, he starts to question his relationship with Harry. Eventually, he makes the choice to leave Harry. There could be a lot of emotional turmoil for all three characters. Harry might feel betrayed, Bella might be conflicted about getting involved with Jacob in such a situation, and Jacob has to deal with the consequences of his choice. In the end, it could lead to a new relationship between Jacob and Bella while Harry has to find his own way forward.
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 Edward, perhaps influenced by some dark magic or a misunderstanding, decides he has more in common with Harry. Maybe he sees Harry's courage and selflessness and feels drawn to that world. He leaves Bella heartbroken, and Bella then has to find a way to move on while Edward starts a new life in the wizarding world with Harry as his new friend or more.
In this type of fanfiction, it could be that Harry has some unresolved issues from his past relationship with Cho. He sees Ginny as a distraction from dealing with those. But as time goes on, he can't ignore the pull he still feels towards Cho. He may leave Ginny when he realizes that he can't move forward in his life without exploring what could have been with Cho again.
In some fanfictions, Fleur might leave Bill for Harry because she realizes that Harry has a certain selfless quality that she admires more. Harry's constant fight against evil and his willingness to sacrifice himself could be very appealing to Fleur. Also, it could be that the fanfiction is set in a situation where Bill is involved in something that Fleur morally opposes, and Harry represents a more morally upright choice for her.
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.