Having trouble accessing my show game of thrones season 1 on apple TV that I purchased years back on my iPad. it is not showing in my library on my TV. I have tried resetting the app and even tried redowndloading it on my iPad but I still see it.

Could it be that age restriction settings on the TV or inside the app block this particular show? Restrict access to content in the Apple TV app - Apple Support

Of course this content should normally be visible in the Library of the TV app, under TV shows (for episodic content).

Do you have other content in your Library that does get listed as intended? (I.e. one particular show vs. everything.)

Do you have other devices where this show does get listed as intended?

If the issue persists, contact the Apple Support staff.

Do you have an Apple TV box? If so, which model? Identify your Apple TV model - Apple Support

Or do you have the Apple TV app on a third party streaming device? If so, what model?

Does your Apple TV use the same Apple ID account as was used for the purchase of this TV show? Library content will only be accessible for matching accounts.

Unable to see purchased movies, why not?