There might be Muggle soldiers who are initially skeptical of Hermione but later become her allies. She could also meet some higher - up military officials who either support or oppose her presence in the army. For instance, a general who sees the potential in Hermione's magical abilities and wants to utilize them for the greater good, or a colonel who is against having a witch in the military due to traditional beliefs.
Hermione may encounter some magical creatures that are somehow related to the army. It could be that there are hippogriffs used for reconnaissance in the fanfiction. And she would have to interact with the handlers of these creatures, learning about their care and how to incorporate them into military operations.
Hermione might also come across some magical creatures that are guarding certain vaults in Gringotts. For example, a dragon that she has to find a way to bypass without getting burned. These encounters would add more excitement and danger to her visit to the wizarding bank.
Well, one possibility could be that Hermione uses her vast knowledge to improve the army's strategies. Maybe she comes up with new spells or ways to defend against dark magic threats that the regular military tactics don't cover.
There's a chance she meets some old Death Eaters who are lurking around Spinners End. This would put her in a very dangerous situation, but it would also make for an exciting plot. She would have to use her wits and magic skills to outsmart them. Or perhaps she meets some of Snape's old school friends who can provide insights into his character and motives.
They could meet American wizards who have a very different style of magic. Maybe some of the native American wizards who have their own ancient magical traditions. These wizards could teach Harry and Hermione about magic that is connected to nature in ways they've never seen before in Britain.
She might meet her old teachers. They would be surprised to see how much she's grown and changed. And of course, her former classmates. There could be the popular girl from school who is now a bit jealous of Hermione's confidence. Or the nerdy boy who has now become a successful scientist and they can have an interesting exchange about different kinds of knowledge, magical and Muggle.
She could meet Bella Swan. They might start off as a bit of an odd couple, with Bella's more reserved nature compared to Hermione's boldness. But they could learn a lot from each other.
She could meet the headmistress of St Trinians. That would be an interesting encounter as Hermione tries to understand the school's rules and the headmistress tries to figure out this strange, book - smart girl. Also, she might meet the troublemakers of the school, those girls who are always getting into scrapes and might see Hermione as either a threat or someone to rope into their schemes.
Perhaps she'll meet older, more experienced students who can act as mentors. These students could introduce her to secrets of the new school that are not easily accessible to newcomers. They might also help her with any homesickness she has for Hogwarts.
There could be new characters introduced, like a nosy neighbor who notices Hermione's odd behavior. This neighbor might try to figure out what she's up to, leading to some comical or tense situations. Also, Hermione might interact with local Muggle kids, and through these interactions, she could learn more about Muggle culture and values.
Another possibility is a jealous student at Hogwarts. There are always students who might be envious of Hermione's academic achievements. They could set up a prank or a trap that goes wrong and ends up hurting her. For example, a student who is tired of Hermione always getting the top grades in Potions might tamper with her cauldron during a class experiment, resulting in an explosion that hurts her.