Combine the rice and chicken broth in a small saucepan. Bring to a boil, cover, and reduce the heat to low. Cook until the rice is tender and the broth is absorbed, then spread the rice on a plate to cool.
Heat the olive oil in a skillet over medium heat. Add the bell pepper, onion, and celery. Cook, stirring occasionally, until softened, about 5 minutes. Add the garlic and chopped Andouille sausage, then cook for 2 minutes. Transfer the mixture to a bowl and let it cool.
Heat the oven to 375°F. In a large bowl, combine the ground turkey, cooled rice, cooled sausage and vegetable mixture, egg, breadcrumbs, Cajun seasoning, Worcestershire sauce, thyme, and black pepper. Mix gently until just combined.
Shape the mixture into a compact loaf in a baking dish. Stir the tomato paste with 1 tablespoon of water, then spread it over the top of the loaf.
Bake until the center reaches 165°F, about 50 to 60 minutes. Let the meatloaf rest for 10 minutes before slicing so it holds together neatly.