A plot could be that Snape is suffering from some sort of post - war trauma that no one else seems to notice. Hermione, being the observant and empathetic person she is, decides to help him. She tries different methods like introducing him to Muggle therapies she has read about, or using calming spells and potions she creates herself. As she helps him, Snape begins to open up about his past, his feelings for Lily, and his experiences during the war, which in turn helps Hermione understand him better.
In a fanfiction, Snape might want to help Hermione when she is wrongly accused of stealing powerful magical artifacts. Snape, knowing her character, decides to use his skills as a Potions master and his knowledge of the castle's secrets to find the real culprit and clear Hermione's name. He could be motivated by his new - found respect for her intelligence and her Muggle - born status which he has come to understand better over time.
Hermione could start by showing her genuine intentions. For example, she could offer to help Snape with his potions research without asking for anything in return. Since Snape is passionate about potions, this might pique his interest and make him less resistant.
A possible plot could be set in a post - war Hogwarts where everything is in chaos. Hermione is at the center of rebuilding the magical knowledge, and Remus is attracted to her intelligence and leadership. Tonks, who has always loved Remus, feels left behind. The story could then revolve around Tonks' attempts to understand Remus' new feelings, Hermione's obliviousness to the whole situation, and Remus' internal struggle between his old feelings for Tonks and his new - found attraction to Hermione. This would create a complex web of relationships and emotions within the fanfiction.
Maybe Snape has a difficult spell he can't seem to master, and as much as he hates to admit it, Hermione's academic prowess makes her the best person to ask for help. He approaches her in a very snarky way, but she sees through his facade and decides to assist him. This could lead to an interesting dynamic where they start to respect each other more.
Perhaps Hermione is injured in a fight against dark wizards while on a secret mission. Snape discovers her and, despite their past differences, decides to help. He uses his skills in dark magic knowledge to counteract the dark spells that have injured her. This could lead to a begrudging respect between them as they work together to heal her and keep the situation a secret from other Hogwarts students and staff.
Their relationship could start off very tentatively. Snape would be his usual gruff self, but Hermione would notice his small acts of help. As time goes on, she might start to trust him more and they could develop a sort of mentor - mentee relationship, with Snape passing on some of his more esoteric knowledge of magic to Hermione.
Maybe Snape is involved in some sort of mystery or danger within Hogwarts that has to do with magic spells. Hermione, with her vast knowledge of spells and her in - depth study of the Hogwarts library, could be a great help to him in deciphering old spells or magical texts related to the situation.
One possible reason could be related to a difficult potion she's trying to brew. Snape is a potions master, and Hermione might be facing an ingredient or a process that she can't figure out on her own. For example, a rare potion that requires precise handling of dangerous ingredients.
Their relationship could start off with a lot of tension. Snape has always had a bit of a prickly relationship with students, especially those he sees as being too much like Gryffindors. However, as they are forced to collaborate, they might find common ground in their love for knowledge. Snape is a highly skilled wizard in many areas, and Hermione is eager to learn. This shared interest could be the starting point for a more amicable relationship.
Another possibility is that she has to help Snape with teaching. Maybe there are some students who are particularly difficult to handle, and Hermione's intelligence and experience as a student herself could be useful. She could help Snape come up with better teaching methods or ways to engage the students more effectively.