Generously season chicken with salt and pepper on both sides; set aside.
Preheat Instant Pot by pressing the Sauté button. Heat olive oil, then sear chicken for 3 to 4 minutes on both sides. Remove and set aside on a plate.
Deglaze pot with ¼ cup of chicken broth, scraping the brown bits from the bottom. Add onion, and carrot and sauté 2-3 minutes until softened, stirring often. Add garlic and cook an additional 30-60 seconds until fragrant. Press Cancel.
Add remaining chicken stock, lemon juice and zest, peas, rice, and parsley, stirring well to combine. Place chicken thighs on top, but do not stir.
Close and seal the lid. Cook on Manual High for 7 minutes, allowing a 10 minute Natural Release, then releasing the remaining pressure by flipping the valve.
Remove the lid and shred the chicken with two forks. Mix everything together, then serve topped with additional parsley, a crack of black pepper, and lemon wedges.