A trope that often shows up is the 'soulmate' concept. The idea that Remus and Hermione are somehow fated to be together, perhaps through some magical bond. This can lead to a lot of romantic and emotional moments in the fanfiction. Also, the 'jealousy' trope can play a role. There could be other characters who are jealous of the relationship between Remus and Hermione, or vice versa, which can create more conflict and drive the story forward.
The 'alternate universe' trope is also common. In some fanfictions, the story might be set in a world where the normal rules of the Harry Potter universe don't apply. For example, there could be a world where age differences don't matter as much, or where Remus and Hermione are brought together in a different context, like they are on a secret mission together and their relationship blossoms during that time. There are also stories that might involve time - travel, where Hermione goes back in time and meets a younger Remus, which adds another layer of complexity to their relationship.