According the the Zimbra Desktop Instructions:
When I click on the "To" the email address list does not pop up or appear.On the Compose page type the email address of the person or persons to whom you are sending the message in the To: field.
• You can click To to look up a person's email address in order to search through your contacts
iMac OS X Version 10.7 Lion
Zimbra Desktop Version 7.1.1 (Build 10917)
Iz Teremka Kennel