This guide, gives a step-by-step to update Teamspeak 3 (3.13.6) 64 bit server on Ubuntu 18.04 and 20.04.
Updated: 16th June 2021
I have presumed you followed my install setup guide here.
Login to SSH as root
Stop your current Teamspeak 3 Server
service ts3server stop
Change to your teamspeak user
cd /home/teamspeak/;su teamspeak
Download Teamspeak, extract it, update and tidy up.
tar xvfj teamspeak3-server_linux_amd64-3.13.6.tar.bz2
cp * -R /home/teamspeak
rm -r teamspeak3-server_linux_amd64
Return to root and start the Teamspeak server
service ts3server start
Check to make you can connect to it, in Teamspeak 3 client.