Hi @ex,
Thanks for the question!
It is not currently possible to have an ongoing sync for contacts in HubSpot and Outlook. The Outlook extension can be used to add new contacts into HubSpot (or update their information in HubSpot), but it will not update the information in your Outlook address book.
If this is something you would like to see implemented in the future, you can search, vote for or post this as a feature request on our ideas forum here: https://community.hubspot.com/t5/HubSpot-Ideas/idb-p/HubSpot_Ideas.
Thank you,
Jenny