This is done in ZWC (Zimbra Web Client)

• Login to your Zimbra account using your browser.
• Click on the Calendar tab
• Right click on the Calendar to be shared
• Select Share Calendar

• Fill in the email field with the address of the person(s) you wish to share your calendar with.
• Set the Role with appropriate permissions.
• Click OK

Those people will receive and email and are required to accept the share.

After they accept the share that calendar will appear in ZWC.

After the calendar has been shared in ZWC it can be shared in Outlook and not require credentials.

Note: This was done in Outlook 2016

The first part is done in ZWC (Zimbra Web Client)

• Login to your Zimbra account using your browser.
• Click on the Calendar tab
• Right click on the Calendar to be shared
• Select Share Calendar

• At the bottom of the Share Properties dialogue under URL right click the link next to Outlook and select Copy Link Location
• Email that link to the person(s) that want that calendar in Outlook.

In Outlook go to the Calendars

• In the top (Ribbon) menu click Open Calendar
• Select From Internet

• Paste the emailed link into the empty field
• Click OK

The shared calendar will now show under Other Calendars in the left pane.

To make the calendar visible you need to check the box next to the shared calendar.