How to insert fork ring tightly?
The part is called centering sleeve. The easiest way to install it is leaving it to the place where it is shown on the screen shot, then pushing it down with a headset spacer as far as it will go and finally installing the dust cap and pushing with it.

It is not supposed support any load, even if it accidentally did with the old fork. Instead, the bearings are adjusted with the headset cap and held in place by clamping the stem around steerer tube.