Hello!
Kind of looks like you are using screen size displacement which is not the best option for animations. If I'm guessing wrong here do let me know :)
Screen size displacement will subdivide your meshes, so that you get that nice intricately detailed displacement, based on the view and the pixel size amount you've set. It's "adaptive". This is especially useful for when you're dealing with still images and you have things in the distance and you don't really want to subdivide them too much because you won't be able to make up the details anyway. Great for still but not the best for animations.
For animations you'll want to switch to world size displacement - that'll do the subdivisions no matter the view point, you'll essentially get uniform subdivisions even if that object is 1px in size and somewhere in the background. Probably not that useful for still images but really useful for animations because the topology will never change hence you won't get any weird geometry popping.
Hope that helps!
