Am assuming your ceiling is gypsum board (sheetrock). Is that correct?

I guess ??

Is your house older, so it would have plaster rather than sheetrock? If so, I would have sheetrock installed over the top of it, and have it all taped and mudded, and then prime it and paint it. It would help if you would post a picture, so we can see what the problem is.

Pictures

Did these post ??

Yes

Great !

Do you know the reason for the cracking? House settling or you have a roof/plumbing leak?

I don’t think there is a leak .. it’s been years

It looks like it is probably sheetrock. It can be repaired, but, there are some suspicious spots, that look like moisture. Do you have an attic? Can you get in the attic? It needs to be inspected to see if there is a roofing leak. Remember roofing leaks, can be up higher on the roof, and run down to a lower spot, so you need to look good. Take a flash light, and look around for any staining on the underside of the roof.

You don't cover cracks, you fix them. Is there a bathroom over your foyer? You could have a minor leak in the plumbing. Water can travel and not be visible right under the source of the leak. This occurred in our previous house. There was a bathroom over the foyer and the leak showed in the ceiling of the living room. When we remodeled the bathroom the source of the water was discovered. It had likely been leaking for years - just a little bit over a long period of time. If you can't DIY you need to hire someone to fix it. It's a multiple step process. Whomever you hire to fix should be able to give you an opinion about whether they think a leak has caused the issue.