Their relationship might also change in a more romantic sense. In a new time, away from the pressures and expectations of their original timeline, they could explore their feelings for each other more freely. Maybe they'd have more time to just be together and get to know each other on a deeper level without the distractions of the battles and events that were going on in their own time.
If they time travel, their relationship could become stronger. They'd be relying on each other in a new and strange situation. Having to face the unknown of a different time period would make them depend on one another for support, both emotionally and in terms of survival strategies.
Another idea is that they travel to a time before they ever met. This allows them to see how things were without their influence. Maybe they find out that small changes in the past have a huge impact on the future. For example, if Pyrrha hadn't been so well - known before coming to Beacon, how would that change the relationships and events there? And Jaune could see how different his life would have been without Pyrrha's initial guidance and friendship.
If Arthur travels back in time and sees Merlin as a young boy, he might develop a more protective feeling towards him. He'd understand Merlin's journey better and their relationship would shift from just king - and - servant to something more like an older brother - younger brother dynamic. On the other hand, if Merlin takes Arthur to the future and shows him a world without Camelot, Arthur might feel a sense of loss and rely on Merlin even more for emotional support.
Their relationship would likely become more complex. Since Harry has only known Lily through memories and stories, actually meeting her in person through time travel would be a shock. Lily would see Harry as a grown man, not the baby she left behind. They might develop a more equal, friend - like relationship as they face the challenges of the time - travel situation together.
Well, if they time travel together, they might become more reliant on each other. In a new and unfamiliar time period, they would be each other's only link to their original time. This could lead to a stronger bond between them.
On the other hand, if Voldemort travels to the future and sees how much Harry has grown and the resistance against him, he might respect Harry in a strange way. He could see Harry as a worthy adversary, which would change the nature of their enmity. Instead of just hating Harry blindly, he might start to understand him better.
Their relationship could become stronger. As they face the challenges of time travel together, they would rely on each other more. Naruto's impulsiveness might be tempered by Shikamaru's strategic thinking, and Shikamaru might become more open to Naruto's bold ideas.
If they travel to a time when their family was intact, they might have a more carefree relationship. Without the burden of the family's fall and all the hardships they faced, they could be more like normal siblings, teasing each other and having fun together. But at the same time, they would know what is to come in the future, so there would still be a sense of responsibility between them.
Their relationship could also become more of a mentor - mentee type situation at times. If they travel to a time when one of them has more knowledge about what's going on, say Trunks if they go to a time related to his future knowledge, he could be like a mentor to Goten, guiding him through the situation. But then in other situations, Goten's natural fighting instincts might lead and Trunks would learn from him. This back - and - forth would change their relationship in a dynamic way.
It might also become more complicated. If they travel to a time when one of them was in love with someone else, like when Elena was still with Stefan in the past, it could create jealousy and confusion. They would have to face these emotions and decide if their current relationship is worth fighting for.
If they travel back in time, their relationship could become stronger as they rely on each other more. They already have a bond in their original timeline, but in a new and uncertain time, they'd have to trust each other even more. This could lead to them confessing their feelings earlier than in the original story.