Another plot could involve Tamaki getting injured during a fight. Shinra then takes it upon himself to take care of her. As he nurses her back to health, they have a lot of time to talk and get to know each other on a more personal level. This could lead to them realizing that they have a lot more in common than they initially thought, and their relationship could grow from there.
In a fanfic, their relationship could also develop through moments of vulnerability. Let's say Shinra has a nightmare about his past and Tamaki is there to comfort him. Or Tamaki has a moment of self - doubt about her abilities, and Shinra gives her an encouraging speech. These moments of showing their true selves and being there for each other can deepen their connection. It's about creating situations where they can be honest with each other and build an emotional bond.
The OC could be a scientist who is working on a new way to control the Infernals without having to kill them. Tamaki is assigned to protect the OC as there are those who oppose this new method. As they spend time together in the lab and during field tests, Tamaki becomes fascinated by the OC's intelligence and dedication. The OC, in turn, is charmed by Tamaki's positive attitude. They might face opposition from within the Fire Force, but their relationship and the OC's research continue to progress.
Another way is through their relationships. In the case of a Tamaki x OC fanfiction, their interactions with Tamaki are crucial. If the OC is initially shy around Tamaki due to her confident and outgoing nature, but gradually opens up, it shows character growth. Also, their relationships with other members of the Fire Force can contribute. Maybe they have a rivalry with one member that forces them to improve their skills, which in turn affects their overall character development.