How to make new columns in SharePoint contact list shown in Outlook interface where the SP contact list is displayed ?

In SharePoint, you can use "Connect to Outlook" to make a Contact list displayed in Outlook.  You can drag in user names from Outlook Contact to the that SharePoint Contact list shown in Outlook interface

The questions is -

when we add a new column in SharePoint Contact list, the column won't show up in that contact list in Outlook as the user record is sourced from Outlook Contact which does not have that column.

Is there a way to sync Outlook Contact with SharePoint Contact so that the additional columns in SharePoint Contact will show up in Outlook Contact?

Thanks for any tips!