If displacement fits into your RAM
What do you mean by this? Is it related to the pixel size of the map? like 1024 x 1024 px?
You have displacement quality controls in the Render Setup > Performance tab under "Displacement".
-If you are using "screen size" mode, your displacement will be calculated only based on your current camera position, so that everything that is outside of your camera view is flat. Also, it will be calculated "intelligently" so that the further areas are less detailed, so in case of animations you will end up with flickering. The lower the "screen size (px)" value, the smaller details are allowed, and the more memory is required.
-If you are using "world size" mode, your displacement will be calculated for the whole object(s), even if they are outside of the camera view. There is also no "adaptivity" in the displacement, so the mesh will be tessellated evenly. This however results in flicker-free animations. The lower the "wold size (units)" value, the smaller details are allowed, and the more memory is required.
The size of the displacement bitmap (e.g. 1024x1024 px or 8k x 8k) should not really matter that much - RAM usage will be similar.
But the render output resolution will matter - e.g. if you render with displacement screen size set to 2px in full hd resolution and in 8k resolution, because in both cases the geometry will be tessellated with smallest detail of 2px allowed.