Set the Instant Pot to "Sauté" mode.
Add olive oil and sauté the onion, carrots, celery, garlic and cook for about 3 - 4 minutes until softened and fragrant. Add dried thyme, rosemary, salt, and pepper to the vegetables. Stir well.
Press cancel then add chicken, potatoes, and broth. Set the Instant Pot to "Pressure Cook" or "Manual High" mode for 10 minutes.
Once the cooking cycle is complete, allow the Instant Pot to release pressure naturally for about 10 minutes. Then, carefully do a quick release to release any remaining pressure.
Stir in frozen peas and let them cook in the residual heat for a couple of minutes.
Combine arrowroot flour and water and stir until dissolved. Stir the slurry into the stew, and set the Instant Pot to "Sauté" mode again. Cook until the stew thickens to your liking, about 5 minutes until thickened.
Taste and adjust the seasoning if needed. Serve the chicken stew hot, garnished with fresh herbs if desired.