Before rushing out to buy that big beast of a card that will run in 4K when your viewing system is still only going to render 1080p at a push.
You are likely better to look at upgrading both card and monitor so that your screen can take advantage of higher refresh rates and a monitor that will do the card justice.
Its like compressed audio and people asking how to uncompress so they can compress the file to a higher bit rate because they think it will be better audio... In this case, your Screen will be the let down, you can't get a better image out of a screen that will only give you a set quality. So it goes without saying that your improvements can be made but you won't appreciate the upgrade until you upgrade your monitor to one that can handle the graphics card.