Heat the olive oil in a large skillet over medium-high heat. Add the celery chunks, carrots and red onion. Cook, stirring occasionally, until the vegetables are slightly softened, about 2 minutes. Add the bell pepper, thyme, paprika, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring, until the paprika is toasted, about 1 minute.
Add the rice to the skillet and stir to coat. Add the tomatoes, black-eyed peas and 1 1/2 cups water. Bring to a boil, then reduce the heat to low. Cover and simmer until the rice is tender, about 15 minutes.
Scatter the okra over the rice. Continue to cook, covered, until the okra is tender and the rice is cooked through, about 5 more minutes. Remove from the heat and let stand, covered, 3 minutes. Fluff the rice with a fork and sprinkle with the celery leaves. Season with salt and pepper.