I'm not sure specifically if there is a well - known 'Harry Potter is the Prime Minister' fanfiction. But given the vastness of the fanfiction community, it's entirely possible. Fanfiction allows for all kinds of crossovers and alternate universes. So, someone might have written a story where Harry Potter, with his magical abilities and heroic nature, steps into the role of the Prime Minister to solve both magical and non - magical problems in a unique way.
One possible plot could be that the Prime Minister has to seek help from the wizarding world led by Harry Potter to deal with a dark magic threat that is seeping into the Muggle world. For example, strange magical creatures are starting to appear in London and causing chaos. Harry Potter and his friends then work with the Prime Minister's office to figure out a way to send these creatures back to their proper magical realm and also put up wards to prevent further incursions.
One interesting fanfic could be where the Muggle Prime Minister discovers the wizarding world in a more personal way, like accidentally stumbling into Diagon Alley. This could lead to a series of comical and also dangerous situations as he tries to understand and navigate this new world while also dealing with his Muggle responsibilities.
The interaction could be initially very tense. The Prime Minister might be skeptical and afraid of Harry Potter and the magic he represents. But as the story progresses, he would start to see Harry as an ally. For example, Harry might have to perform some magic in front of the Prime Minister to prove the existence of the wizarding world, and the Prime Minister would be both amazed and a bit intimidated. Later, they would communicate more freely, with Harry explaining the ways of the wizarding world and the Prime Minister sharing his concerns about how magic can impact the Muggle society.
The position and authority of the cabinet chief and the prime minister in the Ming Dynasty were different. The prime minister was the general term for the highest administrative officer under the ancient Chinese monarch. He had actual power and was responsible for overseeing government affairs. The chief assistant of the cabinet was the first assistant minister in the cabinet. He usually did not have any actual power and only provided some suggestions to the emperor on government affairs. Although the chief assistant of the Ming Dynasty's cabinet was not as famous as the prime minister, he had already become the prime minister in reality. The more powerful cabinet chiefs, such as Yang Tinghe, Yan Song, Xu Jie, Gao Gong, Zhang Juzheng, and others, had the power to command the officials. Whether it was prestige or power, they were even more powerful than the prime ministers of the Han, Tang, and Song Dynasties. But no matter what, the Prime Minister was still not the Prime Minister. This was because the prime minister of the Han, Tang, and Song dynasties had the right to rule the country. The power of the cabinet chief was somewhat unjustified. Yan Song was able to monopolize the government because Emperor Jiajing was superstitious about Taoism and neglected government affairs. Zhang Juzheng was able to monopolize power because Emperor Wanli was young and lacked ruling experience. This kind of power could be taken back by the emperor at any moment, or suppressed by the eunuchs. It would be difficult to do anything. From the point of view of procedure, there was only one eunuch between the Prime Minister and the Chief Minister.
Create complex relationships. Let the Prime Minister form an unlikely alliance with a wizard who is considered an outcast in the wizarding community. This relationship could develop over time and have a big impact on how they both deal with the challenges that come their way. By making the characters' relationships more nuanced, the fanfic becomes more engaging.
There could be a fanfic where the Prime Minister discovers he has some latent magical ability due to his close association with the wizarding world. In this story, he could start learning basic spells and charms, all while trying to keep it a secret from the public. This would add an interesting twist to the typical relationship between the Muggle and wizarding worlds.
Well, one possible plot could be that Harry uses his magic to combat various threats to the country that normal politicians can't handle. Like using spells to stop terrorist attacks or natural disasters. He might also have to hide his magic from the public while still using it for the greater good.
One interesting fanfiction could be where the Prime Minister has to deal with a magical crisis in the Muggle world that is somehow connected to Hogwarts. Maybe the dark forces are using Muggle technology against the wizarding world and the Prime Minister has to work with the Ministry of Magic to stop it.
In this fanfiction, it could be that the prime minister has to work with Harry Potter to prevent a wizard from using magic to influence political decisions. Harry, with his knowledge of the wizarding world, would be the key to uncovering the plot. They might have some initial misunderstandings due to their different worlds, but eventually learn to cooperate. The prime minister could be amazed by the magical creatures Harry introduces to him, like a hippogriff or a phoenix, which would be a completely new experience for him.