One interesting storyline could be them teaming up against a new, powerful alien threat that neither the UNSC nor the Covenant remnants can face alone. They start off distrustful but gradually learn to respect each other's skills and cultures.
Their relationship can be developed through shared battles. For example, when facing a common enemy, they start to rely on each other's unique abilities. Master Chief's superhuman combat skills and Arbiter's leadership within the Covenant structure can complement each other.
One possible storyline could be them teaming up against a new, powerful alien threat that neither the UNSC nor the Covenant can face alone. They have to put aside their differences and combine their unique skills and knowledge. Master Chief's combat expertise and the Female Arbiter's understanding of Covenant politics and technology would make for an exciting partnership.
For Master Chief, his character could be developed by showing his reaction to working with a former enemy like the Female Arbiter. We could see his internal struggle as he has to trust someone from the Covenant. For the Female Arbiter, her character can be developed by exploring her view of humans through her interactions with Master Chief.
A lot of fanfictions also focus on cultural exchange. The Master Chief is from a human military background, while the Arbiter is from the Covenant. Their interactions can lead to interesting cultural exchanges. For example, they might learn about each other's beliefs, values, or military strategies. Some fanfictions may also delve into a more complex relationship where they have to overcome initial distrust or misunderstandings due to their species' past conflicts.
The exploration of different cultures is also a common theme. The Arbiter represents one culture and the Chief represents another. Fanfiction writers like to explore how these two cultures interact. This can include things like differences in combat styles, social hierarchies, and beliefs. It adds depth to the relationship between the two characters as they learn about each other's cultures and sometimes find common ground.
A plot could revolve around a mystery that involves both of their species. The Female Master Chief and the Arbiter start investigating it separately, but their paths cross. As they dig deeper, they realize that their fates are intertwined, and they must rely on each other not only to solve the mystery but also to survive the dangerous forces that are trying to stop them.
You can try fanfiction platforms like FanFiction.net or Archive of Our Own. These sites have a large collection of fanfictions, and you can simply search for 'Master Chief x Arbiter' in their search bars. There are often filters to help you sort by popularity, rating, etc.
Some Halo fan communities on Discord may also have fanfiction channels. Members often share their own works or know of good stories. You can join a few relevant Discord servers and explore the fanfic sections there.
Communication is key. Since they come from different species with different languages, they could start with simple gestures of peace, like laying down their weapons. Then, slowly learn each other's languages or use some form of translation device. As they communicate, they can share their views on war, honor, and loyalty, which are important concepts in both of their cultures. This would help build a deeper relationship.