Ceiling, board replace?

I have a board on my kitchen ceiling which appears to be sagging, I believe that this may just be due to me removing strip lighting and the fixings mush have been helping to hold the board in place. Can I simply (?) remove this board and replace it with another?

If so is it just regular plaster board that is used and do I just need to fit it to the beams with nails?

My intention would then be to fill any gaps and paper the ceiling?

This sound okay?

Best.

sounds spot on to me, though i think i would skim the whole ceiling then paint it.

p.s if anyone on here tells you that you've GOT to screw it, take no notice.

screws are great though, if you have a bouncy joist.