In a medium saucepan, heat the avocado oil over medium-high heat. Add in the onions, carrots, and celery and sauté until the onions are translucent about 7-10 minutes.
Add in the water, salt, and pepper. Bring to a boil. Reduce to a simmer, cover, and cook until the rice has absorbed the water, about 45 minutes. Once the rice is cooked, stir in the cannellini beans and apricots.