Turn Instant Pot on and press the Saute button. Add the sliced carrots, celery, diced onion, minced garlic and butter. Sauté until the onions are soft, about 3 minutes. Turn the sauté setting off. Add the salt, pepper and dried parsley. Toss to coat the vegetables.
Add the whole chicken pieces,the bay leaves, and the thyme to the Instant Pot. Pour 6 cups of the chicken broth over the ingredients. Stir with a wooden spoon. Place the lid on the with the sealing valve closed and pressure cook for 7 minutes.
Allow a natural pressure for 15 minutes and then release the remaining pressure. Carefully twist the lid off away from your face. Remove the hot cooked chicken from the pot and place it in a bowl. Allow it to rest for about 5 minutes nd then shred with two forks.
Pour the instant rice into the Instant Pot and stir with a wooden spoon. Place the lid on the Instant Pot and lock into place. Allow the rice to cook in the hot chicken broth until tender, about 15 or 20 minutes. Remove the lid once again and stir the cooked rice into the chicken soup before serving.