It's well documented (https://support.office.com/en-us/article/differences-between-the-new-and-classic-experiences-for-lists-and-libraries-30e1aab0-a5cc-4363-b7f2-09e2ae07d4dc) that the new experience for SharePoint lists (inc. contact lists) doesn't have the ribbon and therefore there are several key functions not available. Specifically "Connect to Outlook" - which can be used to add a shared SharePoint contact list into Outlook, e.g. for an organisation-wide easily accessible address book.
AFAIK, the only fix is to switch back to classic view. However, considering that classic views are often phased out, is there an alternative way to add a SharePoint list to Outlook? It's been quite a while since the new view was implemented.