Currently, it is not possible to share a contact list (automatically). Our My Contacts feature automatically merges duplicates across all your personal sources and then syncs them back to your personal syncing sources.
However, we now offer FullContact for Teams (beta) which allows for syncing, collaborating, and sharing details. You can read more about it here.
Keep in mind that it is possible to share a list of contacts by exporting them in a .CSV / vCard format. To learn more about exporting contacts, please read here.