how do I establish Apple TV on my Samsung Smart TV that I purchased 2015
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See the following from Samsung Support https://www.samsung.com/us/support/answer/ANS00082624/
The Apple TV app is available on select 2018, 2019, 2020, and 2021 Samsung smart TVs, Lifestyle TVs, QLED 4K and 8K TVs, and the Premiere projector. It is also available on Apple TV, Roku, and Amazon streaming devices. For a full list of compatible devices, check out Apple support. You do not even need to download it because it will appear in the Apps section on your TV.
Note: If the Apple TV or Apple Music app does not appear in apps, then it is not compatible with your TV.
I have another brand of smart TV that does have an Apple TV app -- but I use a Roku as I prefer it (and only cost me $29). https://www.roku.com/products/players