One idea could be Arya using her Faceless Man skills to avenge the wrongs done to her family. She could infiltrate the enemies' strongholds unnoticed and take them out one by one.
The story of Arya Stark as a Faceless Man is complex. After arriving in Braavos, Arya enters the House of Black and White. Her training involves many things. She has to serve in different ways, sometimes cleaning bodies in the temple. She learns the art of poison and how to move silently. However, Arya struggles with completely becoming a Faceless Man because of her strong will and her desire for vengeance. She manages to blend the skills she acquires with her own identity and goals. She's not just a tool of the Faceless Men but uses their teachings to fight for what she believes in, like justice for her family. She's a very unique case among the Faceless Men trainees.
Arya might use her Faceless Man abilities to protect the common folk. She could disguise herself as different people and gather information about threats to the villages. Then she would act to stop those threats, like bandits or corrupt lords preying on the weak.
Arya's journey as a Faceless Man begins when she sails to Braavos. She's drawn to the House of Black and White. Once there, she knocks on the door and is let in, which is the start of her training to become a Faceless Man.
In a fanfiction about Arya Stark being pregnant, she might be in a situation where she has to keep her pregnancy a secret. Maybe she's in a land where her enemies are everywhere, and if they find out, they'll use it against her. She could rely on her skills of disguise and stealth to hide her condition as she tries to find a safe place for herself and her baby.
One idea could be a crossover where Naruto is transported to the world of Westeros. He meets Arya Stark and they team up. Naruto could teach Arya some of his ninja skills, like how to move stealthily like a shinobi. This would enhance Arya's ability to seek revenge on her enemies in a more efficient way.
He could be a wizard who made a deal with a powerful magical entity. In exchange for great power, he lost his face. Now, he appears in the story of Harry Potter, and his presence might be a sign of a greater, more complex plot involving power struggles within the wizarding world that Harry will eventually get caught up in.
One plot idea could be Arya, in disguise, getting close to Tywin as a servant in King's Landing. She could overhear his plans and use that knowledge to try and undermine the Lannisters from within. Another could be a scenario where Tywin discovers Arya's true identity but decides to keep her alive for some strategic reason, perhaps to use her as a bargaining chip against the Starks. And a third idea might be a story set in an alternate universe where Arya and Tywin form an unlikely alliance against a common, greater threat, like a White Walker invasion in the south before the events at the Wall.
One plot idea could be Arya and Jon teaming up to uncover a long - hidden family secret. Maybe there's a lost Stark heirloom that has some sort of power, and they have to go on a quest to find it. Another idea is that they are both sent on a diplomatic mission to an unfriendly kingdom, and they have to use their unique skills - Arya's stealth and Jon's leadership - to succeed.
One plot idea could be that Arya and Aegon meet during their travels. Aegon, with his claim to the Iron Throne, is in need of a skilled ally like Arya. She could help him in his political maneuverings in a way that no one else can, using her skills of disguise and stealth. Another could be a story where they are forced to team up against a common enemy, like a new threat rising in the Seven Kingdoms that neither the Starks nor the Targaryens can face alone. They start off distrustful of each other but gradually come to respect and rely on one another.
There are also fanfictions where Arya is betrayed by someone she thought was a friend. This is a very hurtful situation for her as she has always been cautious about who to trust. When this trust is broken, it can lead to a downward spiral of emotions for her, and it makes for a very emotional read for the fans.