I should add: There is no REVOKE option for "Developer ID Application" certificate type as there is for other certificates types like for example when you edit the "iOS Distribution Certificate".

I just called Apple and learned that because of Apple system limitations you cannot delete "Developer ID Application" certificates. Apparently, the only option is to export the "Developer ID Application" from the old mac and import it to the new one using the Keychain Access. Of course, there are all kinds of new problems and obstacles. Does anybody know how to transfer correctly the "Developer ID Application" certificate from one Mac to another?

Thank you so much! This worked like a charm.