Activate "Screen Space Reflections" in the render tab. And may be you want to use my chnages to your shader. "Specular"s value "0.5" is more physically correct. I also cranked up the IOR value to 1.8, which is the IOR of silver (you will find huge tables
with IOR values for all kinds of materials online).
But the main reason, why the ring is dull grey in the "final" render and shiny in the viewport is: Your world material has the same dull grey color...:)
Even the most shiny silver ring will reflect only the dark when there is no light.
See attachment (the screenshot still has the wrong IOR...sorry)