Arya may become more confident in her abilities with Jaqen's guidance. She could grow from a somewhat reckless girl into a more calculated and strategic assassin. For example, she might learn to better plan her attacks instead of acting on impulse all the time.
At first, it could be a teacher - student relationship, with Jaqen teaching Arya more advanced skills of the Faceless Men. As time goes on, they might become comrades, relying on each other in dangerous situations.
In some fanfictions, there might be a plot where Jaqen actually has a deeper connection to Arya's family than she initially realizes. Maybe he was secretly tasked with protecting her all along. This could lead to a series of revelations and a change in their relationship dynamics, from mentor - student to something more like comrades in a grander scheme.
It's possible that they would go on a mission to uncover some long - lost secrets in the world of 'Game of Thrones'. Jaqen's knowledge of the underworld and Arya's determination could lead them to places like the ancient Valyrian ruins. There, they might find powerful artifacts or knowledge that could change the balance of power in Westeros.
Perhaps in the fanfiction, Arya and Jaqen form an unexpected bond due to the pregnancy. Jaqen, who is usually a mysterious and somewhat aloof character, could show a more caring and protective side. They might have to find a safe place to stay, away from the chaos of their normal lives, and figure out how to raise a child in a world full of danger and intrigue.
I haven't come across a fanfiction with that exact plot. Fanfiction often explores different relationships and storylines in the 'Game of Thrones' universe. While Arya and Jaqen have an interesting relationship, pregnancy isn't a typical aspect explored in mainstream fanfictions about them. It could be that it exists in some more niche or less well - known works, but it's not something I've seen frequently.
To develop the story further, you can introduce conflicts related to the pregnancy. For instance, Arya's physical condition might limit her ability to fight or travel as she used to. This can create tension as she tries to overcome these limitations while still protecting herself and her unborn child.
Arya and Tywin could also interact in a more unexpected way. Maybe in a situation where they are forced to work together for a short time due to some external threat. During this time, Arya has to constantly remind herself of her ultimate goal of revenge while Tywin is constantly on guard against her, yet also seeing potential in her skills for his own purposes.
One great fanfiction is 'The Sisters' Reunion'. It beautifully explores Arya and Sansa's relationship after their long separation. It shows how they learn to trust and rely on each other again, with vivid descriptions of the Westerosi setting.
There's also 'Sansa and Arya's New Adventures'. In this fanfiction, they embark on a journey across the Seven Kingdoms to discover secrets about their family. Along the way, they encounter old enemies and make new allies. It's full of action and the exploration of their sisterly bond.