What kind of account are you talking about, eg POP3, IMAP or Exchange?
If it's an Exchange account then that is controlled at the server end so you'd need to speak to your ISP to get the account updated to change the default.
If it's POP3/IMAP then you can change that within the account settings in Outlook. Go to File, Account Settings, Account Settings..., Change..., and then update the E-mail Address entry to the one you want to be used by default.
Note, I'm assuming you mean you have a single mailbox configured in Outlook since you mention having an additional address added, however you also mention it being default which sounds like you have two setup and you're trying to change which one is used
by default. If that's the case, rather than selecting Change in the Account Settings window, you simply select the account you want to be default and then click "Set as Default". Outlook will then default to using that mailbox when creating new messages
etc.