Turn your Instant Pot to Sauté mode. Add the olive oil and once it’s hot, add the sliced mushrooms. Cook for about 5-6 minutes until the mushrooms start to soften. Then add chopped leek and minced garlic, and cook another ~3 minutes. Cancel the Sauté mode.
Add the chopped carrots, celery, uncooked wild rice, vegetable broth, dried thyme, bay leaf, salt and pepper. Stir gently to combine and ensure the rice is mostly submerged in the liquid.
Close the lid of the Instant Pot and set the steam release valve to Sealing. Select Manual/High Pressure and set the timer to 15 minutes. Wait as the pot builds pressure (about ~20 minutes) then cooks.
After cooking, allow the pressure to release naturally for several minutes (do not quick release unless you’re in a rush). Carefully open the lid when safe.
Stir in the shredded chicken andheavy cream until it’s fully incorporated, giving the soup a creamy finish.
Ladle into bowls and garnish with fresh thyme if using. Serve warm and enjoy.