In ZCS if you are running the Zimbra server with standard Imap and POP services i.e no proxy is running and if you enable ImapProxy then the Zimbra server will detect port conflicts.
The ports 110 and 143 will be occupied by the Imapproxy services.
Tomcat will not be able to start itself and you will receive the following error in catalina.out file:
Error from /opt/zimbra/tomcat/logs/catalina.out:-
Zimbra server reserving server socket port=110 bindaddr=null ssl=false Fatal error: terminating: PrivilegedServlet init failed java.net.BindException: Address already in use
Disable ImapProxy using:-
1) su - zimbra
2) zmprov -l ms `zimbrahostname` -zimbraServiceEnabled imapproxy
[-l option will modify the configuration in LDAP as the normal zmprov command will not run, as tomcat is not running and it will give Java errors.]
Restart Zimbra Services.
Check if the services are running.