One emotional moment could be when Arya sees Sansa again. After all they've been through, the estrangement, the different paths they took. When they meet, all the past grudges are forgotten, and they just hold each other, crying. It's a moment of pure sisterly love and relief that they are both alive and together again.
The moment when Rickon returns, if included in the fanfiction. Sansa and Arya had thought him dead. When he walks through the gates of Winterfell, they rush to him. Sansa holds him tightly, and Arya is jumping around in excitement. Rickon is a bit shy at first but then hugs his sisters back. The joy and disbelief on their faces, the sobs of relief, would make this a very emotional moment in the Stark reunion fanfiction.
When Jon Snow reunites with Bran. Jon left Bran as a young boy, and now Bran is this all - knowing being. Jon kneels down in front of Bran, not fully understanding what has happened to him but still feeling the deep connection of family. Bran simply looks at Jon with his deep, all - seeing eyes and says 'Welcome home, brother'. This simple exchange can be filled with so much emotion as it represents the passage of time and the unbreakable family bond.
A possible fanfiction could start with Arya Stark finally making her way back to Winterfell. She arrives just as Sansa is looking out from the battlements. Sansa's eyes widen in disbelief and joy. They run towards each other and embrace tightly, tears streaming down their faces. Then Bran, now the Three - Eyed Raven, arrives on his sled, drawn by his guards. His siblings are overjoyed to see him, especially when he reveals some of his new - found knowledge about the family's future and the safety of Winterfell.
Perhaps Harry is a Stark and the cave is a place of prophecy. He enters the cave and sees visions of the future of Westeros, including the downfall of his family if certain actions are not taken. He then uses his knowledge from his previous life (if we assume some sort of reincarnation or transfer from his Harry Potter world) and his Stark upbringing to change the course of events. He might form alliances with unlikely characters, train in new forms of combat or magic found in the cave, and ultimately strive to put a Stark on the Iron Throne, all while trying to keep his family alive and the realm in balance.
One possible plot could be that Arya, after all her adventures, finally hears a rumor about Jon being alive. She sets out on a journey to find him. When they meet, Jon is initially shocked to see how much Arya has grown and changed. They share stories of their respective experiences, like Arya's time with the Faceless Men and Jon's resurrection. Then they decide to team up to face the remaining threats in Westeros together.
Another idea for a fanfic is that Arya discovers she's not really the last Stark. There could be a long - lost relative hidden away. She then embarks on a journey to find this person. Along the way, she has to overcome many obstacles and face new enemies, all while trying to keep the hope of the Stark family alive.
She could end up ruling over a part of Westeros. Her skills and experiences would make her a great leader.
It could be that Arya is tape - gagged during a mission gone wrong. She was infiltrating an enemy stronghold but was discovered. Now, she has to figure out how to free herself and complete her mission while being silenced. This would show her determination and survival skills even in a difficult situation.
Well, in fanfiction, the story could be about how Brandon Stark's son grows up in a post - Game of Thrones world. Maybe he has to deal with the remaining political unrest. He could be trained in the ways of the North, learning how to be a strong leader like his father.
It could also focus on her family relationships. Maybe she has a closer bond with Sansa or Catelyn Stark. She could be involved in the family's political struggles, like trying to protect the Stark name during the War of the Five Kings. She might use her knowledge of the North and the secrets beyond the Wall to her family's advantage.
It could be a bastard child of a Stark that was kept hidden for some reason. Maybe for fear of political ramifications or because of some dark family secret.
Another fanfiction could be about Jon Snow (who is later revealed to be Ned Stark's son). In this story, he could fully embrace his Targaryen heritage much earlier. He might form an alliance with Daenerys not as an equal but as a leader, using his knowledge of the North and the loyalty of the Night's Watch to help her claim the Iron Throne in a more peaceful way.