You can set your own MTA or the one from your ISP as RelayHost:
Setting a relay host
Set the relay host in the admin console, MTA tab to point to your ISPs outgoing mail server. Your ISP can tell you the proper value for this. You may have to set the port, as well.
from: Outgoing SMTP Authentication - Zimbra :: Wiki
zmprov ms server.domain.com zimbraMtaRelayHost external.relay.com:#
Works quite well for me. My Zimbra Box uses another Postfix Box in my Network to send out Mail to the Net. The Second Box is configured to use my ISPs MTA as a RelayHost.
ZCS 5.0.6 CE on Linux VServer with Ubuntu 8.04 Hardy Heron behind NAT and using a RelayHost