Heat olive oil in a stockpot over medium-high heat. Add carrots, onion, red bell pepper, celery, ginger, and garlic; saute until carrots soften, about 5 minutes. Stir in curry powder, coriander, and cayenne pepper.
Pour clam juice, tomatoes, and coconut into the stockpot. Bring to a boil; reduce heat to medium and simmer until tomatoes break down, about 20 minutes. Add shrimp. Cover and cook until opaque, about 10 minutes.
Stir rice, okra, coconut milk, cilantro, honey, lime juice, and salt into the stockpot. Simmer until flavors combine, about 7 minutes.