Combine water, pasta, salt, parsley, and pepper in a multi-functional pressure cooker (such as Instant Pot). Seal lid. Select high pressure according to manufacturer's instructions; set timer for 2 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Stir in peas, ricotta cheese, pesto, and Parmesan. Seal lid again and cook on high pressure for 1 minute, allowing 5 to 10 minutes for pressure to build.
Release pressure carefully using the quick-release method, about 5 minutes.