Pat the chicken dry and rub it all over with olive oil, salt, pepper, garlic powder, thyme, and paprika. This helps the skin crisp a bit even under pressure.
Pour 1 cup of the chicken stock into the Instant Pot and place the trivet inside. Set the seasoned chicken on the trivet, breast side up. Add the remaining stock to come halfway up the sides of the chicken.
Seal the lid, set the valve to sealing, and pressure cook on high for 25 minutes. It’s okay if you’re between sizes; a 4-pound bird usually lands around this time.
Allow a natural release for 15 minutes, then quick release any remaining pressure. Carefully remove the chicken to a plate and cover loosely with foil to rest.
Skim off some fat from the surface of the cooking liquid if you can. Turn the pot to sauté. Whisk the flour into 1/4 cup cold water to make a slurry, then whisk that into the hot liquid to start the gravy.
Stir and simmer until the gravy thickens to a nice, pourable consistency. Stir in the heavy cream and taste; adjust salt and pepper as needed.
Carve the chicken and spoon or ladle the gravy over the meat. If you like, serve with mashed potatoes or roasted vegetables for a complete, comforting plate.