Ashkenazi custom is to remove any object not connected to the body – even a dangling necklace, which surely doesn't invalidate immersion. This custom is based on the Rema on Shulchan Aruch 198a, and is binding for Ashkenazi women.
These would be grounds to regard the nuvaring as a chatzitzah, and it should therefore be removed prior to immersion lechatchilah.
However, bedieved, if it is difficult to remove or if a woman forgot to remove it, there may be room for some leniency for two reasons:
1) The ring is positioned in a hidden place (beit hastarim), which is regarded more leniently in certain situations
2) The ring is not stuck in one place, but rather can be moved around, theoretically allowing the water to reach the entire area.
Therefore, if you are unable to remove the ring yourself for immersion, you should push the ring around while preparing for immersion, so that it is not stuck in one place, and then immerse with the ring inside.