Edit the rsyslog file

sudo vi /etc/rsyslog.conf

add the following. Change out the IP address for your remote syslog server IP address.

The syntax for this has changes. Newer recommended way is

*.*  action(type="omfwd" target="192.0.10.5" port="514" protocol="tcp"

Old Syntax

## rsyslog Server
*.*     @10.0.10.5:514

https://www.rsyslog.com/sending-messages-to-a-remote-syslog-server/

Restart the rsyslog service and check your remote log server.

systemctl restart rsyslog