12GB+ of dedicated VRAM is recommended for 4K gaming but some games can run on less even with higher settings. i guess it may depend on what you want to play and how much future proofing you want.
My work computer now has 2 4k monitors that I use with my MacBook
Moving my desktop over to these new monitors so need to upgrade the video card, league of legends struggled on 4k on these monitors so that's what im trying to sort out as cheaply as possible since that's only pc game I would play as of late.