One common theme is the transformation of their initial enmity. They start off as rivals or at least not on friendly terms, and then slowly realize they have feelings for each other. For example, in many stories, they first clash because of their different personalities or because of competition within the camp.
One great piece of 'Percy and Clarisse fall in love fanfiction' is 'Love in the Midst of Battle' on FanFiction.net. It really explores how their initial animosity could transform into love. The author does a wonderful job of showing Percy's growing respect for Clarisse's strength and Clarisse's newfound softness towards Percy.
Yes, there are quite a few. You can start by looking on fanfiction.net. There, you'll find a variety of stories exploring their relationship. Some might focus on how they gradually fall in love during their adventures in the Percy Jackson universe, while others could be more about the challenges they face as a couple within the context of the demigod world.
Their relationship could develop as comrades. They might start off disliking each other but as they face challenges together, like battling powerful foes or solving mysteries in the demigod world, they learn to tolerate and then respect one another. It's a development based on mutual respect for each other's abilities.
One common theme is the idea of opposites attract. Percy is often seen as more easy - going and Clarisse is tough. Their relationship development around this difference is a big theme. Another is the concept of mutual respect growing over time. They start off not really liking each other in the original books, so in fanfiction, the journey to respect and then love is explored.
One idea could be that Percy and Clarisse are forced to team up on a quest outside of Camp Half - Blood. At first, they bicker constantly like they used to, but as they face various challenges, they start to see each other's strengths. For example, Percy realizes Clarisse's battle skills are invaluable in a fight against a group of powerful monsters. They gradually become friends and learn to respect each other more than ever before.
Maybe Clarisse has her own reasons. She might see Percy as someone who needs protection in the complex world of the fanfiction setting. It could be that she has a soft spot for him deep down, or she feels a sense of responsibility towards him for some unspoken events in the story.
One common theme is rivalry -turned - friendship. They start off not liking each other much in the original stories, so many fanfictions explore how they can move past that initial animosity. For example, they might be paired on a mission and slowly realize they have more in common than they thought.
I really like 'Clarisse and the Quest for Honor'. In this fanfiction, Clarisse goes on a solo quest that challenges her in ways she never expected. It's full of action and also some really interesting interactions with minor characters from the Percy Jackson universe that you don't often see in the main series.
A theme that frequently appears is the exploration of their individual growth. Clarisse may learn to be more understanding, and Percy might gain more respect for Clarisse's abilities. Also, the theme of redemption can be seen. If they've made mistakes in the past, fanfictions sometimes show them making up for it through their actions together. And there's also the theme of mutual respect. As they get to know each other better, they start to respect each other's skills and personalities more.