Switch the Instant Pot to the sauté mode and wait for the olive oil to become hot.
Now, add the chopped onions, and chopped carrots, together with chopped celery. Now, sauté for 3-4 minutes until they turn soft.
Add chicken pieces and uncooked wild rice along with chicken broth. Add salt and pepper.
It is time to cover the Instant Pot and press the valve to set the pressure to high for 25 minutes only.
After the time goes off, just let the pressure out naturally for 10 minutes or so, and when most of the pressure has gone out, lift up the pressure valve to let the rest out.
Take the chicken out of the pressure cooker and shred it with a couple of forks. Then add the shredded chicken back to the pot.
(Optional) Pour in some cream or coconut milk to make the soup thicker and creamier. Wait for 2 minutes for the flavors to infuse in soup.
Correct the taste of the dish with salt or pepper, if needed.
The soup is served hot, sprinkled with fresh green parsley, with a piece of crusty bread or a side salad.