You can export that public key from your "old" install, and then import it into the new keyring. Yes, the key would have been previously imported and signed by that user's key. You have to decrypt the incoming encrypted email; which requires you to enter your passphrase, so that your private key can be decrypted for decryption of the email.
If you are sure that you only want encryption with this one individual, you can disable the default PGP messaging policies, and create one that will only encrypt to that one email address, and take no action on any email sent to any other address. It sounds like this may be what was done with the old installation. You may want to look at the old PGP Messaging policies that show how the PGP proxy will act on outgoing email.