Using third party Android apps you can now sync your contacts and calendars from Zimbra Cloud to your mobile device. Below is the screenshot for the process.
Ref KB: https://kb.diadem.in/how-to-configure-email-account-in-android-gmail-app_1209.html
For synchronize webmail calendars or contacts with Android need to download Open sync app. It is a free open source sync app which is used to synchronize calendars and contacts with Android.
Step-1
Download the Open sync app using the mentioned link:https://play.google.com/store/apps/details?id=com.deependhulla.opensync&hl=en_IN&gl=US
Welcome to OpenSync page will be open >> Now click on "+" sign to add account
Step-2
To add account select the Login with URL and user name >> click on Login >> Click on Create Account
e.g. https://zcs.diademtech.in:443 (URL of your Zimbra server)
Step-3
Now your Account will be created >> You need to allow the App and give it the required permissions.
Step-4
Click on the OpenSync permission >> Click on both Request Calendar Permissions and Request Contacts Permissions >>
Give the Allow Permissions >> Click on your account OpenSync >> Select all the relevant contacts and calendars for the Sync process
Step-5
You can change the Sync interval time from the Settings option >> Click on Contacts Sync. interval and Calendar sync interval >> Select the sync intervals.
Step-6
Now go back to the previous section and Click on Sync option. Your contacts will sync from the zimbra server when you compose a new email.
Step-1
Open Webmail >> Calendar >> New Appointment >> schedule an appointment >> Save and close
Step-2
FromOpenSync app >> click on Sync >> Check the Calendar app from the android device and you can see the appointment will be synced to your phone.