Default Ports Used by Zimbra

You may choose not to allow remote connections to all of these. In a multi-node environment, all nodes will need access to the ldap server or servers (389) and to the logger server (514), mta nodes will need access to lmtp on all mailbox nodes (7025), mailbox nodes will need admin port access to other mailbox nodes (7071).

External Access

These are ports typically available to mail clients.
25      : smtp [mta] - incoming mail to postfix
80      : http [mailbox] - web mail client
110    : pop3 [mailbox]
143    : imap [mailbox]
443    : https [mailbox] - web mail client over ssl
465    : smtps [mta] - incoming mail to postfix over ssl (Outlook only)
587    : smtp [mta] - Mail submission over tls
993    : imaps [mailbox] - imap over ssl
995    : pops [mailbox] - pop over ssl
7071  : https [mailbox] - admin console

Internal Access

These are ports typically only used by the zimbra system itself.
389     : ldap [ldap]
636     : ldaps [ldaps, if enabled]
7025   : lmtp [mailbox] - local mail delivery
7047   : conversion server
7306   : mysql [mailbox]
7307   : mysql [logger] - logger
7780   : http [mailbox] - spell check
10024 : smtp [mta] - to amavis from postfix
10025 : smtp [mta] - back to postfix from amavis

System Access

22        : ssh
514      : syslogd [logger] (udp)

Reference : Wiki Ports