In the Instant Pot, add the chicken broth, red curry paste, brown sugar, and fish sauce. Turn on the saute setting and heat just until curry paste and brown sugar are melted and blended into the broth. Turn off the saute setting.
Add minced garlic, chopped onion, sliced celery, shredded carrots, red pepper, yellow pepper, chicken, and garbanzo beans. Stir all together until well blended. Add enough water to cover all ingredients.
Place the lid on the Instant Pot, and make sure the pressure valve is set on SEALING. Press the MANUAL button and set the time to 6 minutes. Allow the pressure to build and release naturally for 5 minutes, then do a quick release by turning the valve to VENTING and allowing all the pressure (steam) to be released and the float valve to a dropdown. Open the lid, stir the soup, and allow the soup to cool down.
Add the coconut milk and stir well. Serve over rice in a bowl and sprinkle with your favorite toppings on top.