In normal circumstances once a change is made in Active Directory, it should be synced over to Igloo the next time the ILST is run.
If this is not happening, we will need to dig into the specifics of you configuration. This is best done through a Support Ticket.
Can I have you submit a ticket to email@example.com and include the following:
- The Trace log for the latest ILST run
- The email addresses of any affected users (new and old)