Obviously, Harry Potter himself is a very important character as the story revolves around him learning family magic. His friends like Hermione and Ron might also be important as they could support or help him in his journey of learning this magic.
It could be an older relative who was thought to be dead but actually has been living in seclusion, waiting for the right time to teach Harry about their family magic. This relative might have a vast knowledge of the family's magical traditions and spells.
In some fanfictions, Harry might learn family magic that has to do with time manipulation. His family could have had a special talent for seeing into the past or future. As he delves into this magic, he has to learn to control it carefully, as misusing time - related magic can have serious consequences. He may use this new - found magic to prevent certain disasters or to gain knowledge from the past that could change the course of the wizarding world.
In this type of fanfiction, a great plotline could be that Harry stumbles upon a hidden family grimoire. Inside, he finds magic that was thought to be lost. For example, there could be spells for creating protective shields that are stronger than any known spell. Or perhaps he discovers family magic that is related to time - travel, which he then has to learn to control carefully so as not to disrupt the timeline. This discovery of family magic would add a whole new layer to his character development and his role in the wizarding world.
It might be a story where Harry delves into the family magic in order to solve some sort of mystery. For example, he could be looking for a way to defeat a new dark force and realizes that the family magic holds the key. He could learn new forms of magic related to protection or divination that are unique to his family.
Perhaps it's a magical crystal that enhances his ability to communicate with magical creatures. This would be quite unique as it would give him an edge in dealing with things like thestrals or unicorns, and open up new storylines in the fanfiction. Harry could use this crystal to understand their needs and gain their help in various situations.
Harry grows by becoming more self - reliant. Learning Black family magic is likely not an easy task and he has to figure things out on his own. He becomes more confident in his abilities as he masters new spells and magic techniques.
In the fanfiction, it could be that Harry's learning of Black family magic unlocks a new power within him. This power could be related to his connection with the Black family through Sirius. He may then use this power to fight against the rising dark forces in the wizarding world, in a way that is different from the traditional magic he has been taught.
He might learn about hidden magical talents in his family. For example, perhaps there were ancestors who could communicate with magical creatures in a unique way that was lost over time.