How to set a SNMP trap receivers in vCenter Server

First, you must register the External SNMP server in the list of SNMP trap receivers in vCenter Server. This list is accessible in the vSphere client -> vCenter Server Settings -> Administration menu.

Change localhost to the IP or DNS name of your server.  Change 162 to the defined or customer port of your SNMP server.  Change public to the SNMP server string name.

That is all that is needed for the configuration.  Now you need to setup alarms to send to the SNMP trap.

Configure the Alarms

After you have setup the external SNMP server, vCenter Server can send SNMP traps to it. There are  alarms in vCenter Server that are configured to send traps by default. So your SMNP server should receive alarms as soon as you have the SNMP setup.

Some default alarms are defined on the root of the vCenter Server inventory (1), from where they propagate to all child objects. If you go to the Alarm management tab (2), you can check the definitions (3) of the default alarms. Selecting a specific alarm (4), you can check on its Actions tab (5) if sending SNMP traps is active for this specific alarm (6). Image and  text from blog.vmware.com

From here you can create custom alarms to send to your external SNMP trap servers.