Heat the olive oil in a skillet over medium heat. Add the ground turkey and cook until browned, breaking it apart with a spoon as it cooks.
Transfer the cooked turkey to the slow cooker. Add the onion, carrots, garlic, white beans, chicken broth, thyme, salt, and pepper.
Stir everything together, then cover and cook on low for 6 hours.
Stir in the kale during the final 30 minutes of cooking so it softens without losing its color.