How can I watch AppleTV on old 2013 smart Samsung TV

you can purchase the apple tv box

I have one connected to my 2009 sony non smart tv

works like a charm

Rudegar’s solution is the only way that will work on a2013 Samsung. Some Samsung models beginning in 2018 would allow you to download the app.

If you don't want to spend the money on an ATV (though I recommend it), you can also look into a Roku or Fire TV stick.