It all depends on how big the object will be in the rendering and how big will be the rendered image itself, in other words, how many pixels will have to cover your texture. 2K displacement might be enough if you're rendering to HD resolution and/or the object in picture is pretty small. I'd suggest to try increase displacement texture resolution to 4K and see if that helps with the issue. Also it's worth to note that usually it's not a good idea to have very high contrast in displacement textures (sharp transition between whitest and darkest pixels), you will get much nicer displacement if you will slightly blur the texture.
