If you save the scraps of leeks with roots from the grocery store, you can regrow them to a surprising size by leaving them in water for a few weeks.
They'll reach a point where they'll stop growing if left in only in water, so you could transfer them to soil. Here are some leeks I grew in water and then transplanted into small terracotta pots. Note that there are 5 leeks in this picture and a celery is hiding among them.
Be careful to not overwater them since their roots may start rotting. You can choose to bottom-water the leeks if you place them in a shallow tray and water the tray. In this picture, I used the plastic lid of a food takeout container as a tray.
After a while, I noticed their roots were crowding the sides of the pots, so it was time to transfer them to a larger container. Here they are in a one-gallon felt grow bag.
They'll eventually outgrow this container too if all goes well. You can plant them in larger containers, of course. It's up to you when you'd want to harvest them again!