This guide, gives a step-by-step to update Teamspeak 3 (3.13.2) 64 bit server on Ubuntu 18.04 and 20.04.
I have presumed you followed my install setup guide here.

Step 1:
Login to SSH as root

Step 2:
Stop your current Teamspeak 3 Server

service ts3server stop

Step 3::
Change to your teamspeak user

cd /home/teamspeak/;su teamspeak

Step 4:
Download Teamspeak, extract it, update and tidy up.

wget https://files.teamspeak-services.com/releases/server/3.13.2/teamspeak3-server_linux_amd64-3.13.2.tar.bz2
tar xvfj teamspeak3-server_linux_amd64-3.13.2.tar.bz2
cd teamspeak3-server_linux_amd64
cp * -R /home/teamspeak
cd ..
rm -r teamspeak3-server_linux_amd64
rm teamspeak3-server_linux_amd64-3.13.2.tar.bz2

Step 5:
Return to root and start the Teamspeak server

exit
service ts3server start

Step 6:
Check to make you can connect to it, in Teamspeak 3 client.