as said above, if you let a domain expire then you lose all rights to it.
if you're lucky, you can still get it by making a new contract for it.
unfortunately there are a number of domain grabbers that automatically check for expired domains and purchase them as soon as they can, in order to redirect the traffic to their own sites.
In a lot of cases they even offer to sell the domain back for an extra fee for them.
you'll have to check if your old domain is still expired or already purchased by someone else, and then you can try to get it back depending on its status.
in some cases you might be able to get it back by contacting the hosters support claiming that you accidentally forgot to pay on time.