Outlook contact card not updating
You can find more details about that method in the guide: Search and Replace for Contact fields.
If you want a more direct or advanced approach within Outlook itself, then you can also use a Search and Replace add-in.
We recently had this happen to a recent client’s Lync Server. For example, a user’s work phone number is changed in AD. (This service is called the User Replicator Configuration.
Looking inside of Active Directory I did not see any where to add an explicit extension and no place looked to be appropriate for that.
If you install the Office ADMX templates, you can customize which fields are displayed on the contact card.