How to renew an expired keypair with gpg

What is the best way to **renew a gpg key pair when it got expired** and what is the reason for the method? The key pair is already signed by many users and available on public servers. - Should the new key be a subkey of the expired private key? - Should it be signed by the old (I could try to edit the key and change the date of expiration to tomorrow)? - Should the new key sign the old?