Hdmi

If your computer and TV has an HDMI socket then it's a simple case of using a M/M (Where M is M.A.L.E) HDMI cable to connect the two.

You may have to adjust the input on the TV to use the HDMI input.

LibreELEC is intended for dedicated HTPC devices so Kodi (on LibreELEC) runs full-screen and outputs to the primary display device (whatever that is) and there is no GUI support for running with multiple-monitors (or laptop screen + HDMI output). It can be done from the command line, but that's more advanced. Another option for a laptop could be forcing the display output in the BIOS.

If you want GUI multi-monitor support, use Windows or a conventional distro like Ubuntu.