When you are lucky enough to get freshly harvested carrots, with carrot tops still attached, use the greens as you would fresh parsley.
As soon as you get them, cut away the tops, give them a rinse and shake them out or spin them in a colander. Loosely wrap them in a clean dish towel and store in your produce drawer. They’ll last even longer (and perhaps not be forgotten) if you store them in a food storage container that allows for air to circulate underneath.
They should do fine for several days until you think of something clever to do with them!