I've added a new domain to a Business Essentials license with the status now showing setup complete. The plan is to move to the new domain in the future. To test I've also added an alias to a user with the new domain e.g. firstname.lastname@example.org but not yet set it as the primary. The issue is when sending an email to email@example.com I get an access denied error i.e.
If you have recently set the DNS records and added the mail alias to the mailbox then it can take some time to propagate (Global DNS propagation is 72 hours). I would leave it a few hours and then send to the mail alias again. If it doesn't work in this case then I would double check the DNS records, ensure that the domain is showing in the accepted domains in the Exchange Admin console, and that the alias is on the mailbox in the Exchange Admin console. If all of this is, then wait one day and try again. If this still isn't working, let us know and we'll investigate
Hope that answers your question!
Best Response confirmed by
David Magee (Occasional Contributor)