In certain occasion’s server’s main IP may get black listed due to some reasons. In this we can change the exim outgoing IP, instead of the blacklisted one.
Please follow simple steps below;
1 : Stop exim.
2 : Open exim configuration [/etc/exim.conf] file with vi/vim.
3 : Search ‘remote_smtp’ section below TRANSPORTS CONFIGURATION.
4 : Delete or comment out line containing ‘interface’ and ‘helo_data’ and add the new ‘interface’ with the new IP address.

It should look like as follows:
================================================
;remote_smtp
;driver = smtp
;interface = x.x.x.x # Change with your new IP.
================================================
5 : Save the changes and quit from conf file.
6 : chattr +ia /etc/exim.conf [otherwise exim will overwrite the changes we made]
7 : Restart exim.
Don’t forget to set rDNS for the new IP to point a valid FQDN.