Another storyline could be that the dragon egg has some sort of connection to Arya's past or her family. It could hold secrets that she uncovers as she tries to hatch it. For example, it might be linked to the Targaryens in a way that Arya doesn't expect, and this discovery could change her understanding of her place in the world of Westeros.
One possible storyline could be that Arya, being the resourceful character she is, tries to figure out how to hatch the dragon egg. She might embark on a journey to find ancient knowledge or a sorcerer who could help her. Maybe she faces many challenges along the way, like being hunted by those who want the egg for themselves.
Perhaps Arya gets the dragon egg in a mysterious way, like finding it in an old, forgotten vault. Once she has it, the egg starts to show signs of hatching early on. This attracts the attention of various factions in Westeros. Some might want to protect Arya and the egg, while others see it as a threat to the current power balance. Arya then has to use her skills as a faceless man to keep the egg safe and deal with the political intrigue that follows.
In a fanfic scenario where Arya finds a dragon egg, it could change the entire course of the Game of Thrones world. Maybe she would try to hatch it in secret, using her skills of stealth. If she succeeded, she could become a powerful force. She might use the dragon to protect her family or seek revenge on her enemies. However, she would also have to face the challenges of hiding and training a dragon in a world full of political intrigue and danger.
The dragon egg could introduce a new side of Arya. She might become more patient, as hatching an egg is not an immediate process. She would have to wait and take care of the egg, which is different from her usual fast - paced, action - oriented life. This could also lead to her developing more diplomatic skills, as she would need to deal with people who are interested in the dragon.
A fanfic about Arya finding a dragon egg could start with her stumbling upon it during one of her adventures. For example, she might find it in an old, forgotten castle. Then, the story could focus on her attempts to keep it safe. She could hide it in her belongings and try to find someone who might know about dragon eggs. The story could also show her internal struggle, as she has to balance her new discovery with her existing goals like revenge.
The origin of the egg might be a mystery left behind by some ancient civilization in Westeros. It could have been hidden for centuries and the Starks just stumbled upon it. Another possibility is that it was smuggled out of Essos by someone who thought the Starks could keep it safe. It could also be a relic from a time when dragons were more common in Westeros, and the Starks were meant to be the ones to revive their power.
In a fanfic where Arya gets captured, she might be used as a bargaining chip. Her captors could try to exchange her for something valuable, like a strategic location or a large sum of gold. Maybe they want to use her to manipulate the Starks.
She might get a small but fierce dragon, like a young and agile one. It could be a dragon with black scales, which would match Arya's dark and mysterious nature.
She could change the fate of her family. Since she knows what will happen in the future, she could stop the execution of her father, Ned Stark. This would have a huge impact on the political situation in Westeros. The Stark family might gain more power and influence, and the War of the Five Kings might not even happen or at least take a very different form.
Well, in the world of 'Game of Thrones' fanfiction, the possibilities are almost endless. Since the show and books have such rich lore and a large cast of characters, it's not surprising that someone would write a fanfic where Arya hatches a dragon. This kind of plot would likely involve some sort of magic or unforeseen event that leads to Arya coming across a dragon egg and then having it hatch. It could also potentially change the entire course of the story in the fanfic, as Arya with a dragon would be a very powerful force.
If Arya is sent to the past, she might first try to find a way back to her own time. But in the meantime, she could end up influencing key historical events. Maybe she'd get involved with the Targaryen rule and change the course of their downfall. Or she could befriend some of the great warriors of the past and learn new fighting techniques that she could bring back with her if she ever returns to her own time.
One of the main storylines is Arya's pursuit of revenge. After her family is brutally massacred, she sets out to kill those responsible. She travels across Westeros, learning the ways of the Faceless Men to become a more effective assassin.