how do I add a title to my library on my iPad?

Library contains your purchases and rentals, so the literal answer here is to buy or rent the content in question.

Per Apple: The Library pane in the Apple TV app includes your purchases and rentals organized by category, playlists you’ve created, and home movies you’ve manually added to your library.

Mac can import content such as home movies into the Apple TV Library, but I don't know that iPad or iPhone can directly perform that task, and don't see any indication that the iPad app can import.

The previously-mentioned +Add button is where your shows of interest are queued.

I think this is how you would do it. Find a show or series that you want to watch and then tap the Add icon in the upper right.

I haven’t added titles in the app, I just search for what I want to watch and then watch it.

Which library and which app might you be referring to?

An iPad that's still running iOS 10 is old, and likely can't be upgraded to current iPadOS software. Apps will increasingly be requiring newer versions of iOS or iPadOS, too. There's no hardware upgrade available as well, only a newer or new iPad.

I wasn’t sure and that’s why I italicized “think”. Can you point out the documentation that tells you that you can add titles to the library? The only titles that are in my library are movies, videos and TV shows that we bought in iTunes.

Ron42nm wrote:

how do I add a title to my library through the app

on my iPad?

What library?

You’re welcome. I was curious if there was some documentation that I was not aware of.