Microsoft has an article on how to do this as well, in case this is not exactly what you need: https://support.office.com/en-us/article/Share-a-contacts-folder-with-others-ce5a40d1-bc9f-4f5d-a2aa-5ec388573821?ui=en-US&rs=en-US&ad=US
Sharing a folder, including a local contacts group, is a two-step process.
Step One: right-click the folder in Outlook and choose Properties.
Step Two: You will get a dialog similar to this.
Step Three: Click Add and type in the name of the user you wish to share the folder with. Select the user and click Add -> or double-click them so they show on the Add line at the bottom.
Step Three:Once returned to the previous dialog, select the user you have added and then the desired permissions from the Permission Level drop-down.
Reviewer - Allows visibility into the folder but no editing or creating of items. This is most often used for auditing.
Author - Allows visibility plus creation and editing of items the user created, but not other users items. This is most often used for shared calendars and mail folders where multiple users need to be able to create events.
Editor - Allows visibility plus creation and editing of all items. This is most often granted to managers/supervisors of a team calendar or mailbox.
Owner - Allows full permissions to all items.
The other selections allow for more granular control and you can set the desired permissions individually.
Step Four: Once the desired users have been added and permissions set click OK to close this dialog.
For sharing anything but a calendar there is one last step to complete.
At the root of the mailbox containing the items to share should be a folder showing just the email address. Left-click to select it and you should get a similar summary view.
Step Five: Right-click this folder and select Folder Permissions.
Following the same process as above for adding permissions, add the users you want to share with. Instead of selecting a permission level from the drop down, for this folder you only want to set the Folder visible right.
This permission grants the ability to see into folders below the top level, but does not grant any permissions to the contents of those folders. This does not make any email, contacts or calendar items visible.
Step Six:To add a mailbox or folder that has been shared, the person being granted access needs to tell Outlook to connect.
Click File, Account Settings, Account Settings.
Step Seven:Under Account Settings, make sure you have selected the account which was granted permissions and then select Change.
Step Eight: Under Change Account select More Settings...
Step Nine: On the dialog that appears, select the Advanced tab and then Add...
In the next dialog, enter the email alias (the part before the @ sign) of the person that has granted you permissions to their mailbox, folder, etc and click OK until you are out of all dialog boxes.
In Outlook you should see that user as a new line on the left. Clicking it to expand it should then show the folders you have been given access to.
If the folder has not shown up within a few minutes you may need to restart Outlook.