If in a different version, Arya's love story with Gendry could have been more fully explored. They could have gotten married and ruled over Storm's End together. Arya would bring her skills and intelligence, while Gendry his strength and leadership of the people there.
In an alternate story, Arya might fall in love with a foreign prince she meets during her travels. This prince could be from Essos, and he would introduce her to a different culture. Their love story would be about bridging two different worlds, with Arya having to decide between her Westerosi roots and this new life with him.
Their relationship could develop in a very complex way. At first, Arya would be full of rage towards Tywin. However, if she were to be captured by the Lannisters and Tywin were to show her a different side of himself, perhaps a more paternal side (even if it's just a ploy), Arya might start to question her hatred. On the other hand, Tywin might see Arya as a potential asset, someone he could mold in his own image. This could lead to a relationship that is part mentor - mentee and part captor - captive, with a lot of power dynamics and emotional turmoil.
As Queen of the North, Arya's character would transform significantly. Her wild and independent streak would still be there, but she'd learn to channel it in a more productive way. She'd start to understand the importance of traditions and how they can be used to unite the people. Her relationship with power would be complex. On one hand, she'd use it to protect the North, but on the other, she'd be cautious not to let it corrupt her. She'd develop a more regal presence, but still keep her roots as a Stark. Her skills as a spy and assassin would be used in more strategic ways, like uncovering plots against the North and eliminating threats without causing unnecessary chaos. And she'd have to learn to balance her personal desires with the needs of her kingdom.
Arya's character might develop in terms of her leadership skills. From being a lone wolf, she has to become a leader. She'll learn to make decisions for the greater good of Winterfell, not just for her own survival.
In a time - travel fanfic, Arya's character could develop a sense of timelessness. She has seen so much death and destruction in her own time. But by traveling through time, she might start to see the bigger picture of the cycle of life and power in Westeros. This could make her more philosophical, and perhaps she'd be less driven by revenge and more focused on the long - term well - being of the realm.
Aegon could develop his combat skills under Arya's tutelage. He has been more of a political figure in the making, but Arya would teach him how to fight in a more practical and street - smart way. This would not only make him more confident but also change his perspective on power. Arya, on the other hand, would develop her diplomatic side. Aegon's knowledge of courtly manners and politics would rub off on her. She would learn to use words as weapons, in addition to her physical skills, which would be a great asset in her future endeavors.
Arya's identity as a Stark would be more deeply ingrained in her. She would start to embrace all the values that the Starks stand for. She might even try to teach these values to the people of the North. Her development would also involve her coming to terms with her past as a Faceless Man. She would decide how much of that part of her should be part of the new Stark legacy she is building.
She might become more confident in her earlier years. In the original story, Arya faced many hardships that made her grow in a certain way. But if she goes back in time, having the knowledge of future events, she could be bolder in her actions and decisions from a young age. For example, she might be more assertive in dealing with Sansa when they were kids, and not let Sansa's girly ways get to her as much.
Arya would likely become more diplomatic. Since she's marrying Daenerys, she'd have to deal with more political situations. She might learn to use her skills in a different way, not just for revenge but for the good of the realm. Daenerys, on the other hand, would become more in touch with the common people through Arya. Arya's experiences growing up among the smallfolk would influence Daenerys's decisions.
Their relationship often develops through shared experiences. For instance, when they face a difficult battle together, it deepens their trust in each other.
Arya Stark started her life in Winterfell. She was different from her sister Sansa. Arya was more of a fighter. When the Lannisters attacked her family, her life changed drastically. She witnessed a lot of death and destruction. Arya then journeyed far and wide. In Braavos, she trained with the Faceless Men. This training was tough and made her a more dangerous person. Later, in the final battles for Westeros, Arya played a crucial role, like when she killed the Night King and saved the world from the Army of the Dead.