I guess it would depend on what the relish is meant to accompany? Sounds like it would go well with something porky - maybe a pork loin, roasted with....? If so, you might want to pick up an herb/spice used there (like a small amount of rosemary) to meld the flavors. Otherwise, to be honest I don't know that you'd need to add anything, beyond S&P. Sounds like the relish already has a good spectrum of intense flavor - sweetness from the beets, acid from the vinegar, heat/pungency from the horseradish - another element might be overkill. Maybe just some chopped chives for color and a dash of onion-ness?

Maybe something smoky like a teeny bit of paprika, or use smoked salt instead of plain? Horseradish goes well with smoky flavors, and the acid will keep it from getting out of hand.

Cumin goes well with beets, but I don't know about the rest.

I might try some fresh dill ...

fennel

Fresh or bottled horseradish? I'd see how it tastes alone, and if it needs anything, go with the mustard, or maybe with allspice, depending what you're after. Might need a pinch of sugar/other sweetener, too.

Hi AJ--I might add some chives and parsley--I agree that sage is unappealing and I don't like caraway at all. You could also consider adding cinnamon if you're trying to bring out some sweetness. Maybe some celery seed? (or leaves? I love celery leaves as an herb.) Sounds delicious just as it is.