Combine turkey carcass, onion, carrots, celery, and water in a multi-functional pressure cooker (such as an Instant Pot). Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 45 minutes. Allow 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 15 minutes.
Pour liquid through a strainer and discard all solids. Refrigerate for 8 hours or overnight. Skim fat from the top and discard. Use stock within 3 days or freeze for up to 3 months.