There is no surefire way to do this, as it depends on how your particular terminal is configured. However, you can generally accomplish this by using the "--app" or "--app-window-type" command line flags when opening your terminal. For example:
This will open a new window that functions as a separate application instance. You can also try using the "--app-window-type=popup" flag, which may provide more consistent results.
If your terminal is not configured to support the above flags, you may need to investigate other options, such as running multiple instances of your terminal program.