According the the Zimbra Desktop Instructions:

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
When I click on the "To" the email address list does not pop up or appear.

OS
iMac OS X Version 10.7 Lion
Zimbra Desktop Version 7.1.1 (Build 10917)

Iz Teremka Kennel