Exim is no longer available as a standard package, but as with most pieces of Linux software, it’s still only a few commands away. If you want to install Exim to use, or just to try, all you need do is:
Install the EPEL (Extra Packages for Enterprise Linux) repository:
wget http://download.fedoraproject.org/pub/epel/6/i386/epel-release-6-5.noarch.rpm rpm -i epel-release-6-5.noarch.rpm
Install the Exim package
yum install -y exim-mysql
Disable Postfix (the default MTA)
service postfix stop chkconfig postfix off
Set Exim as the default MTA
alternatives --config mta
And finally start Exim
chkconfig exim on service exim start
You should now be running Exim, and probably want to visit the official documentation site.