My TV is a 2013 model. How can I get the Apple TV app to set up?

You need a device such as a Apple TV to watch it. You can find a list of devices in https://www.apple.com/apple-tv-app/

If you meant to say Apple TV + then please review https://www.apple.com/apple-tv-plus/

To learn about the different TV offerings Apple has please navigate to www.apple.com/tv

Samsung currently only support TVs as far back as 2018. You would need to contact them to inquire if any other models will be supported.

However, you can also use a Roku or Firestick to access the TV app, or purchase an Apple TV box.

Apple TV app - Devices - Apple (CA)