Well, perhaps Percy witnesses hazing within the NCIS New Orleans unit. She might be conflicted about whether to get involved or stay out of it, especially if the ones doing the hazing are her friends or colleagues she respects. Or, she could be the target of hazing that is more psychological, like being excluded from important cases or being given menial tasks on purpose. This could lead to her feeling isolated and trying to prove herself in different ways.
In a fanfic about Percy and hazing in NCIS New Orleans, it could start with Percy being excited to join the team but quickly realizing there's an unspoken culture of hazing. Maybe she's made to do embarrassing tasks in the name of 'initiation'. As the story progresses, her character could develop as she tries to change this culture. She might start by talking to a sympathetic senior agent. Along the way, there could be twists like some of the hazers having their own reasons for their behavior, such as trying to test Percy's loyalty to the team. This could lead to a complex web of relationships and character growth for Percy and those around her.
One possible plotline could be that Percy is a new recruit and faces hazing from some of the other agents. She then has to find a way to deal with it, either by standing up to them or reporting it. Another could be that there are rumors of hazing in the past involving Percy, and the current team has to investigate it while also dealing with their relationships with her.