Normally the TV (and monitor) will be advertising a 'preferred mode' in its EDID data and the OS will probably be selecting that mode or a mode that both support. If it isn't (and some TV's don't, or don't do it properly, or even lie) then the OS doesn't know what to do with it or selects one that the TV doesn't actually support. Often that's things like the TV claiming it can do 4096x2160@60p (which is apparently "cinema 4k") but can actually only handle that for 30p.
The other thing that has screwed me in the past are garbage HDMI cables. The easiest thing to try is a different cable. Many cheap/older cables are not spec'd for 4K60p and while the TV may report that in their EDID the cable can't deliver it.
If the OS is using X11 or Wayland will change how you configure the mode. I forget off the top of my head what the exact commands are, but that should hopefully be enough to search for help for your OS. If you figure out the commands just drop it down to FHD and go up from there. Using the CLI will let you do it via SSH and not be dependant on the screen because ng available.
