Startup Crontab
This simple method will simply start your TeamSpeak server instance when your server has finished booting. Consider using a Systemd Unit if your system supports it for more advanced features.
Pretty much all Linux distributions support this method as crontab is installed on most distributions by default. If it is not installed it will be available on most package managers and a simple "yum/apt install crond" should work
Add a line like the following to your crontab (run "crontab -e" as your TeamSpeak user to get to the crontab editor on your system)
@reboot /home/teamspeak/teamspeak3-server_linux-amd64/ts3server_startscript.sh restart