[dgamez]

Just put the script on any directory of the server filesystem, set the owner to zimbra and run it as zimbra user. For example:

su - root
chown root:zimbra /opt/zimbra/zsync_ad.sh
chmod 750 /opt/zimbra/zsync_ad.sh
su - zimbra
/opt/zimbra/zsync_ad.sh

Then, you can schedule it with cron.