ᐅ Insulation for cavity between ceiling joists

I am in the middle of renovating our single-family house. The roof will get a completely new insulation, even though I do not plan to use the attic as a living space.
There is a continuous cavity filled with a white insulation material of unknown type in the ceiling between the first floor and the attic. I want to remove all the old material and am now wondering whether I need to insulate the floor-ceiling structure between the floors again afterwards, or if it is sufficient to insulate only the roof properly?

You do not need to insulate the ceiling between floors; insulating the roof surfaces is sufficient. Since the mentioned ceiling will then be within the insulated building envelope, cavity insulation would also be unnecessary.