Export Gmail contacts 

1. Sign in to Gmail.
2. At the top left, click Gmail > Contacts.
3. Click More > Export… .
4. Choose whether to export all contacts or only one group.
5. Select the Outlook CSV format (for importing into Outlook or another application)
6. Click Export.
7. Choose Save to Disk > OK.
8. Select a location to save your file, and click OK.

Import contacts to Zimbra

1. Sign in to Webmail Zimbra.
2. On top menu, click Preferences
3. At the left sidebar, click Import / Export
4. In the Import section File field, browse to locate the contact .csv file to import. (File that you have exported from gmail previously)
5. Select the type of contact file that is being imported. If you are not sure, select Auto-Detect.
6. Select the destination for this file. Select an existing address book to add the contacts or create a new address book to import the file. Click OK.
7. Click Import.
8. Click OK.