Place peas in a small bowl and let sit out to start defrosting.
Select "Saute" on Instant Pot. Add oil and saute onion, carrots and garlic for 2-3 minutes until onion is translucent. Add kielbasa and ham and saute another 2-3 minutes until lightly browned.
Add tomato paste and ketchup; saute for a minute. Add rice and stir to coat. Add reserved shredded chicken and piquillo peppers. Toss to coat with sauce. Add 1 cup reserved chicken broth. Season to taste with salt, if desired.
Select "Cancel," then seal Instant Pot and cook for 4 minutes at high pressure. Natural release 10 minutes; then quick release. Add olives, capers and peas. Toss well, then seal Instant Pot. Let stand 10 minutes before serving.
Adapted from Serious Eats.