Turn Instant Pot to Sauté mode. Add butter or olive oil. Cook onion, carrots, celery, and garlic until soft and fragrant.
Place chicken on top of the veggies. Add rinsed wild rice, thyme, parsley, salt, and pepper. Give a gentle stir.
Add chicken broth and make sure nothing is stuck to the bottom of the pot.
Seal the lid and cook on high pressure for 25 minutes. Let it naturally release for 10 minutes, then quick release the remaining pressure.
Remove the chicken carefully, shred it with two forks, and return it to the soup.
Stir in heavy cream or half-and-half for a creamy finish. Taste and adjust seasoning as needed.
Ladle into bowls and enjoy warm.