TeamSpeak3 systemd service file tested with TeamSpeak version 3.12.1

teamspeak.service

[Unit]
Description=TeamSpeak3 Server
Wants=network-online.target
After=syslog.target network.target local-fs.target

[Service]
WorkingDirectory=/home/ts3server/teamspeak3-server_linux_amd64
User=ts3server
Group=ts3server
Type=forking
ExecStart=/home/ts3server/teamspeak3-server_linux_amd64/ts3server_startscript.sh start license_accepted=1
ExecStop=/home/ts3server/teamspeak3-server_linux_amd64/ts3server_startscript.sh stop
PIDFile=/home/ts3server/teamspeak3-server_linux_amd64/ts3server.pid
Restart=always

[Install]
WantedBy=multi-user.target

Create the file /etc/systemd/system/teamspeak.service with the above as its content.

Then to set up the server do something like (tested on Ubuntu 18.04 server):

adduser --disabled-password --disabled-login --shell /usr/sbin/nologin ts3server 
cd /home/ts3server
wget https://files.teamspeak-services.com/releases/server/3.12.1/teamspeak3-server_linux_amd64-3.12.1.tar.bz2
tar xf teamspeak3-server_linux_amd64-3.12.1.tar.bz2
chown -R ts3server:ts3server .
chmod -R g+s .
systemctl start teamspeak

If all goes well and it starts without issues, you can enable it to start automatically with:

systemctl enable teamspeak

To get the latest TeamSpeak 3 server or to upgrade the current installation get it from https://teamspeak.com/en/downloads/#server

Then cd to /home/ts3server, wget the latest .tar.bz2, untar it and restart the service with systemctl restart teamspeak

Isn't Type=simple better solution? This way systemd monitors the process and you also get the stdout output from the teamspeak server in the journalctl output.