No, it is not appropriate. 'Detroit: Become Human' is a game with complex themes about androids and humanity. Writing sexual fanfic involving its characters goes against the intended nature of the work and can also be considered disrespectful to the game's developers and the wider fan community.
A great Kara Detroit: Become Human fanfiction could be set in an alternate universe where Kara is a detective - like android. She uses her unique skills and empathetic nature to solve crimes that involve both humans and androids, and in the process, she challenges the existing prejudices between the two groups.
You can start by looking on fanfiction websites such as Archive of Our Own (AO3). It has a large collection of Detroit: Become Human fanfictions, and you can easily search for ones specifically about Kara. Just use the search bar and type in 'Kara Detroit: Become Human' and a bunch of relevant stories should pop up.
First, understand the characters well. Kara is kind - hearted and protective, so your OC should interact with her in a way that makes sense for her personality. For example, if your OC is more brash, there could be some initial conflict that then develops into a deeper connection.
Their relationship can be developed by having them face tough situations together. For example, when they are in a fight against anti - android forces, Luther protecting Kara and Kara relying on Luther can deepen their bond.
One idea could be Kara and Luther trying to find a safe haven for all the androids in a post - apocalyptic Detroit. They could face various challenges like human gangs who are against androids, and they'd have to use their unique abilities to protect the other androids they are leading.
You could focus on her journey of self - discovery. For example, write about how she adapts to the human world and learns about emotions. Maybe describe her interactions with other androids or humans in a non - sexual, friendly or mentorship - like way.
One popular plot theme is the unlikely alliance between Connor and Kara. They come from different paths in the game's world, but in fanfiction, they might team up to protect other androids. For example, they could work together to rescue a group of androids from a dangerous situation in a CyberLife facility. Another theme could be the exploration of their emotions towards each other. As androids starting to feel, they might develop a unique bond that goes beyond just friendship or comradeship. It could be a slow - burn relationship where they gradually understand each other on a deeper level.