Set the Instant Pot to Saute and add the olive oil. Let it heat for a couple minutes.
Add the onions and cook for 3 minutes.
Add the carrots, bell pepper and celery and saute for another 2 minutes.
Stir in the broth, wild rice, thyme, rosemary, salt and pepper.
Turn the Instant Pot to off. Put the lid on, lock it and put it on the rice setting. Set the time for 12 minutes.
When the Instant Pot is finished manually release the pressure. Add the coconut milk and shredded turkey to the pot, and stir. Put the lid back on and let the soup sit for 5-10 minutes.