Our family typically grazes for hours!
Keep replenishing it (not filling it) with scaldingly hot soup. You could try seating it on a cloth-covered warming tray, but my hunch says that wouldn't do much.
Jenny, and what a lovely tureen it is!!! One could look at it all day long. My guess too is that it will be difficult to keep the soup hot for a long time. Have you considered serving the soup in something else, and perhaps making a punch or eggnog to showcase the tureen? That might be easier (and the tureen will stay on the table longer).
I don't think it will help for hours, but you can get considerably longer warm-time by filling the tureen with scalding hot water, let it stand for five minutes or so, then drain and add the soup. If you want to go for a long time then perhaps fill the tureen half way and replenish it later.
If it's a cream soup you will want to be careful about keeping the temperature at a safe level.
I have a similar tureen and I've never found the answer. The only way I use it is to serve everybody at the same time either at a sit-down dinner or a buffet with a server (me) attending the soup. Frankly, I find it to be a pita when having a group large enough to merit the size of the tureen.
I have a porcelain soup tureen that I love (it's modern, but same idea) - but unfortunately, I now use it mostly to serve cold/room temp soup, for the same reason. I think Le Bec Fin is right that the only way to serve hot soup in it over a long period is to keep replenishing.
I use an electric hot plate, set on the lowest setting. Make sure to stir the soup from the bottom of the tureen because it will be the warmest.