Sure, here is a simpler and more natural version: "A good relationship needs understanding, support, and companionship."

It is a perfect sentence that needs no improvement. Instead of "a good relationship requires", you could also say "Good relationships require" "An ideal relationship requires" "A working relationship rests on (or 'is built on')"

This is already pretty simple and natural, but less formal might be "a couple needs to work together to be happy".