Follow these steps: 1. Stop your old server instance (Do not kill it! Or else you will not be able to start your new server for the next 2-3 hours!)
These are official supported ways. to shutdown the whole server.
All ways will shutdown the whole instance and will report, that slots are not used anymore.
All operation systems:
The ServerQuery command serverprocessstop.
click me to get an "how to use the Query Interface with Putty"
Right-click into the Server Tray Icon -> Then press Exit
The command ./ts3server_startscript.sh stop if your server was started with ./ts3server_startscript.sh start
2. Make a copy of the existing ts3server.sqlitedb to have a backup in case something bad happens.
*Make a backup of your TS database in MariaDB/MySQL in case you do not use SQLite