Hi Ultraviolet and welcome to GoY. I am not sure if I fully understand your question but here goes. You start leeks on in cells or small pots. You plant them out in the ground they are to grow in when they are about the diameter of a pencil. The soil that was in the cell or pot can be used again as the roots are, hopefully, with the leek not in the soil.

In my experience leeks need to be grown in the ground in a light soil that was manured for a previous crop but has not been freshly manured. The do not grow well in pots.

So you just lift the leeks as you need to use them and then grow a crop of something like potatoes in that area of your garden the following year.

Thanks to Moongrower and Plantmaiden. I hope this is the right place to say my thanks. I will learn slowly!
But my question about the roots left behind - I meant after harvesting! I have JUST dug up some leeks from last year which have survived through the winter. And in flowering pots if I try to freshen them up with more soil - can I re-use the soil which is full of little white wormy roots?

I'm afraid I cannot reciprocate with any advice for anyone else.

If you grew your leeks in flower pots then better to put that soil on the veg garden or a flower border and use fresh soil in the pot this year. Make sure you give the pot a good clean too. Leeks grow much more easily in the ground.