Heat 2 tablespoons olive oil in a large pot over medium-high heat. Add the sausage and cook, stirring occasionally, until browned, about 3 minutes. Add the celery, onion and bell pepper, season with salt and cook, stirring occasionally, until the vegetables soften, 3 to 5 minutes. Add the tomato paste and Cajun seasoning and cook, stirring occasionally, until the vegetables are coated, about 1 minute. Add the rice and cook, stirring, until coated, about 1 minute.
Add the diced tomatoes and 5 cups water to the pot. Increase the heat to high and bring to a boil. Reduce the heat to a simmer, cover and cook until the rice is tender and the sauce thickens, 10 to 15 minutes.
Stir the beans and chicken into the pot and cook until warmed through, about 1 minute. Top each serving with celery leaves and drizzle with olive oil.