Add onion, celery, chicken, and 1 cup of the water to the pressure cooker.
Cook on high pressure for 3 minutes (if using chicken breasts) or 8 minutes (for thighs). Quick release the pressure.
Add sausage, rice, bouillon, and the remaining ⅓ cup water. Stir gently to combine.
Cook on high pressure for 0 minutes. Let pressure release naturally for 10 minutes, then quick release any remaining pressure.
Remove chicken, shred it, and return it to the pot.
Stir everything together. Season with salt and pepper to taste. Serve hot.