Set Instant Pot to Sauté and heat oil; cook onion, carrots, and celery until softened, about 4 minutes.
Add garlic and cook 30 seconds until fragrant. Stir in chicken pieces.
Pour in chicken broth, add bay leaf and thyme, and scrape any browned bits.
Lock lid, set to Manual/Pressure Cook on High for 7 minutes.
Quick-release pressure carefully. Stir in pasta (or rice) and frozen peas; set to Sauté and cook until pasta is tender, about 6–8 minutes.
Remove bay leaf, season with salt, pepper, and parsley. Serve warm.