Remove the tops and compost or dry them to use as carroty seasonings in future soups or stews.
Store the carrots in cold water in the fridge for a week, or washed and in a bag or Tupperware for months. We’ve heard that white varieties of carrots are notably good keepers, but one year we kept a bag full of regular orange carrots in our fridge for the whole winter, perfectly edible except for a gradual bit of flaking of the skins. Not a big deal when we were just using them for soups and stew.