Set the Instant Pot to saute and add the olive oil. Cook the onion, garlic, carrots, and celery for 3 minutes until the onion softens.
Add the chicken breasts, chicken broth, salt, and black pepper. Stir once, then secure the lid.
Cook on manual high pressure for 10 minutes. Allow a natural release for 5 minutes, then quick release any remaining pressure.
Remove the chicken breasts, shred them with two forks, and return the meat to the pot.
Stir in the orzo. Set the Instant Pot to saute and cook for 6 minutes, stirring often, until the orzo is tender.
Turn off the heat. Stir in the lemon juice, lemon zest, and parsley. Taste and adjust salt if needed before serving.