Combine chicken, chicken broth, water, coconut cream, garlic chile paste, coconut aminos, lime juice, salt, ginger, and basil in a multi-functional pressure cooker (such as Instant Pot(R)). Close and lock the lid. Select Soup/Broth function according to manufacturer's instructions; set timer for 30 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the slow-release method according to manufacturer's instructions, about 10 minutes. Release remaining pressure using the quick-release method, about 5 minutes. Unlock and remove the lid. Serve soup in bowls and sprinkle with fresh cilantro.