Best Storage:
Fridge
Keep dry (wash as you use it) and store in an airtight container in your fruit & veg crisper to prevent transfer of smells from the leek to other foods in your fridge.
Freezer?
Yes
To freeze, firstly wash thoroughly as leeks can be quite dirty. Chop up stem section and blanch for approx. 1 minute. Lay out onto baking paper lined tray to flash freeze, then transfer to a container and keep in your freezer. The leaves and ends can also be frozen and added to a container for later use in making homemade stock.
Use it up!
Once defrosted use in cooking.
Use it all up: Don’t throw away your leaves! All of your leek can be used – cut the roots off to replant and grow another, and then use the stems and leaves in cooking.