Purchase a TV Series as a gift

Unfortunately, that is currently only supported on devices with iOS 17.1.2 or earlier.

You may give feedback to Apple about that. Feedback - Apple TV App - Apple.

Gift apps, media, and more from Apple - Apple Support

Just FYI for everyone reading this. Apple updated their support document the day iOS 17.2 was released to indicate it will no longer be possible to gift movies & shows on Apple devices running newer versions of software:

You can't gift movies or TV shows on a Mac or Windows PC, on an iPhone running iOS 17.2 or later, on an iPad running iPadOS 17.2 or later, or on an Apple TV running tvOS 17.2 or later.

Gift apps, media, and more from Apple - Apple Support

I encourage everyone in this thread who wants to see gifting be introduced as an option to submit feedback to Apple here: www.apple.com/feedback or here: www.feedbackassistant.apple.com (the latter one I've actually received more responses to my feedback if that matters to you).

My feedback IDs for feedback I've submitted are as follows. You should reference them in your feedback submissions to indicate a broader desire to Apple:

• iOS & iPadOS: FB13680039
• macOS: FB13680043
• tvOS: FB13680045
• visionOS: FB13680046

In the meantime, while not as convenient as if Apple would just add gifting support in the Apple TV app, there are a few workarounds I've found:

• If you have a Windows PC, you can still use the iTunes app to view, wishlist, and gift movies and tv shows in the iTunes Store. Download iTunes for Windows here.
• If you have a Mac, you can download virtualization software to run Windows. Parallels will work for free, but may charge you after the initial trial ends (I'm not sure because my business pays for a Parallels license so I don't know what happens when the trial expires).
• If you have an iOS, iPadOS, or macOS device running iOS or iPadOS 17.1 or macOS 14.1, or earlier, you may still be able to access movies & shows in the iTunes Store from the iTunes Store app or the iTunes Store tab in the Music app.
• If you have previously wish listed movies and shows in the iTunes Store previously, you can still technically find and rudimentarily "browse" the movies and tv shows section of the iTunes Store in the iTunes Store app on iOS by clicking "View your Wish List" on the Movies & TV Shows tabs and then hunting and pecking through the movies/shows in your list and related movies/shows to find movies and shows. This is the crappiest of all the workarounds as it assumes you've wish listed the movies/shows (or related movies/shows) you plan to gift in the future.

Yes, I know none of my workarounds are idea for Apple users who always keep their devices running the latest software and haven't wish listed before, but just throwing them out there in case someone is desperate enough to need to access gifting for some reason – know that you still can.

Another thought is simply buying an Apple gift card as explained in the above link.