Select the Sauté function on your Instant Pot and add the olive oil.
Add the ground turkey and cook for 5-7 minutes, breaking it apart with a wooden spoon until browned.
Stir in the diced onion, bell pepper, and celery. Continue to sauté for 10-12 minutes until the vegetables are softened and slightly caramelized.
Add the minced garlic, tomato paste, chili powder, cumin, smoked paprika, sea salt, and black pepper. Stir constantly for 2 minutes to toast the spices.
Pour in the tamari and chicken bone broth, using a spatula to scrape any browned bits off the bottom of the pot to prevent a burn warning.
Add the diced tomatoes (with juices), kidney beans, and black beans. Stir well to combine.
Secure the lid and set the valve to the Sealing position. Select Manual/Pressure Cook on High for 15 minutes.
Once the cooking cycle is complete, allow the pressure to release naturally for 20 minutes before venting any remaining steam.
Open the lid and stir the chili vigorously; the beans and turkey will thicken the liquid into a hearty consistency.