There could be. Fanfiction writers often come up with the most creative and unexpected crossovers. Harry Potter's world is full of magic and adventure, and imagining him protecting Queen Elizabeth could lead to some really interesting plotlines. But you'd have to search through various fanfiction platforms to find one like that.
One possible plot could be that dark wizards are planning to use Queen Elizabeth as a symbol to gain power in the Muggle world. Harry Potter, being the hero, gets wind of this plot and uses his magic to secretly protect her. He could use spells like the Fidelius Charm to keep her location hidden from the dark wizards.
Harry would likely be very curious about the court and its people. He might use his magic in small, discreet ways to amuse the courtiers, like making a flower bloom in his hand. He would probably be polite and respectful, but also a bit of an outsider. His different style of dress and his magic would make him stand out, and he'd have to explain himself carefully to avoid being seen as a threat.
I'm not sure if there are many highly recommended ones. Fanfiction can be a very niche area, and combining 'Harry Potter' with Queen Elizabeth is rather unusual. You might have to search through various fanfiction platforms very thoroughly to find something that stands out.
A possible scenario is that Queen Elizabeth has a magical artifact that has been passed down through generations in the royal family. This artifact draws the attention of Harry Potter and his friends. They come to her palace to investigate, and she becomes involved in their adventures. She could offer them resources and protection in the Muggle world, while they introduce her to the wonders of the wizarding world.
She could completely transform the Ministry of Magic. Given her experience in governing, she might restructure it to be more efficient. For example, she could create new departments to deal with things like the proper handling of magical creatures in a more humane way. And in terms of the education system, she might introduce a more comprehensive curriculum that includes not only magic but also Muggle studies from a historical and cultural perspective.
It could be about Queen Elizabeth somehow being a part of the wizarding world in the 'Harry Potter' series. Maybe she's a secret witch or has some connection to Hogwarts.
In this fanfiction scenario, Harry Potter would likely experience a very different upbringing. He might be exposed to the high - society life of the British royalty. He could receive a top - notch education in a very formal and traditional setting, different from Hogwarts. Also, he may have to adapt to strict royal protocols while still having his magical abilities, which could lead to some interesting situations where he has to hide his magic from the public eye but still use it for good within the royal household.
It could be a very interesting fanfiction. Maybe Queen Elizabeth could be a secret witch in the Harry Potter universe. She could use her magic to rule Britain in a different way, perhaps with the help of Hogwarts' magic. For example, she could use spells to improve the economy or protect the country from dark wizards.
It might entail Queen Elizabeth as a character in the wizarding world. She could be a guest at Hogwarts, and all the students are curious about her. She might give a speech about leadership and how it's similar in the Muggle and wizarding worlds.