How do I update a CentOS server's time from an authoritative time server?

Use the ntp daemon. Run yum install ntp and ensure that the service is started via ntsysv or chkconfig ntpd on.

To get an immediate sync, run ntpdate time.apple.com (or something similar).

You need to install and configure ntp.

yum install ntp
chkconfig ntpd on
ntpdate pool.ntp.org
service ntpd start

should get things set up and running. You may find that the ntp package is already installed and just needs configuring.

Yes.

NTP.

yum install ntp
chkconfig ntpd on

Do an initial sync, with

ntpdate pool.ntp.org

and start the time daemon with:

/etc/init.d/ntpd start

You'll need to configure ntpd for the server. I suspect it is already installed but needs to be configured. Note: if it is a virtual server, you probably have the option of syncing with the virtual host.

For centos 7.x installation:

yum install ntp
systemctl enable ntpd

initial sync, with:

ntpdate pool.ntp.org

start the daemon with:

systemctl start ntpd