How do I fix a peeling ceiling?

Wendy,. You need the seams retaped and spackled, then painted. Go to Home Advisor for an experience person, that does this kind of job. Aloha!

https://homeguides.sfgate.com/retape-wall-ceiling-joints-26573.html

Before you tape and bed the old ceiling, I think you need to have the foundation inspected, then the roof. If the foundation has shifted in the last eighty year, then the beams or joists may have shifted also. The foundation and other damage needs to be repaired first. If the roof has shifted because of the foundation or beams, then the roof may need shoring up, also. Often, the foundation people or roof people will recommend that you wait six months to a year before you repair cracks in the walls and ceilings because further settling the first year may cause more cracks. When you get to the right place, then try to screw the old ceiling back to beams and studs. Scrape all the peeling pieces off—that’s probably the old bedding, or plaster that covers the places where the Sheetrock or plywood meet. You use a special kind of plaster to fill in the spaces, then put the tape over, smooth all that out, and let the ceiling (or walls) dry. The next day, usually, you prime the ceiling with white paint, then paint it with the permanent color when the primer is dry. Please do not use popcorn ceiling as a texture. It is hard to get off and almost impossible to repair to match the rest of the ceiling. Best of luck with your old house. I think we should renovate as many of these older houses as we can. ☺️

Wendy,. You need to have the sheetrock-nailed again, and taped, spackled, before you paint. Aloha!