Set the Instant Pot to Sauté – More/High. Season chicken thighs with salt on both sides.
Add olive oil to the pot. Place chicken thighs skin-side down and cook for 5–6 minutes until golden. Flip and cook for another 5–6 minutes. Remove the chicken from the pot and set aside.
Add cherry tomatoes, roasted red peppers, chickpeas, harissa paste, and grated garlic. Stir to combine and scrape up any browned bits.
Nestle the seared chicken thighs back on top of the mixture and sprinkle with za’atar.
Seal the lid and Pressure Cook on High for 10 minutes. Allow a 5-minute natural release, then flip the valve to release any remaining pressure.
Remove the chicken and check the sauce consistency. If it’s too runny, set to Sauté and cook for a few minutes until thickened. Season additionally, if necessary.
Spoon the sauce around the chicken and top with crumbled feta, more za’atar, and plenty of fresh cilantro and oregano. Serve warm.