Turn the Instant Pot to sauté. Add a little olive oil and toss in onion, garlic, carrots, and celery. Cook for 3–4 minutes until soft and fragrant.
Add the chicken, chicken broth, Italian seasoning, salt, and pepper. Close the lid, set to pressure cook high for 10 minutes.
Do a quick release, remove the chicken, and shred with two forks. Return the shredded chicken to the pot.
Stir in the tortellini and cook on sauté for about 5 minutes until tender and cheesy.
Add the cream and fresh spinach. Stir and let it sit for 2 minutes. Taste and adjust seasoning as needed.