Turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function. Add sausage and cook until caramelized and fat is rendered, about 4 minutes. Add onion, celery, garlic, thyme leaves, and pepper. Cook for 3 more minutes. Cancel Saute mode.
Add sauerkraut, potatoes, chicken broth, and hard cider to the pot. Close and lock the lid. Select High pressure according to manufacturer's instructions; set timer for 8 minutes. Allow 10 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes.