Add oil, carrots, celery, onion, salt and pepper. Cook, stirring frequently, until onions are translucent, about 5 minutes.
Add garlic and continue to cook, stirring, for one minute or until fragrant.
Add broth, water, chicken, rice, thyme, bay leaf, and rosemary. Secure lid and turn valve to "seal." Set Instant Pot on Manual (or "pressure cook," depending on your model) for 11 minutes. Quick release pressure when done cooking by turning valve to vent. Remove chicken to a plate; remove and discard bay leaf.
Shred chicken with two forks, or chop into bite sized pieces and return to pot.
Add peas and parsley, stir to combine. Taste and adjust seasoning for salt and pepper. Add more chicken broth or water if soup is thicker than you like it.
Substitute or add additional vegetables, if desired or stir in baby spinach with the peas.
Use boneless skinless chicken thighs instead of breasts, or stir in rotisserie chicken with peas.