Outlook® stores all of an email address' emails, calendar information, contacts, tasks, and notes in a PST file. You can export the PST file from your current address, and then import it into your new address after it's been set up.
You cannot export contacts in your Hosted Exchange Email account's Global Address List and must manually recreate them.
PST file, select Replace duplicates with items exported, and then click Finish.You can now import the PST file. For more information, see Importing Your Information into Outlook.