When movies were previously offered in HD on the iTunes Store, and later offered in 4K, then users should get the 4K version automatically. Just look for the 4K badge. (The SD version stays SD, if one purchased that.) (A redeemed code or reciprocal service copy may stay how it was, without automatic upgrade.)
There is no discount available if you purchased a prior release elsewhere, nor if you somehow need to re-purchase through Apple. There is no discount available for bundles that may include a previous purchase through Apple.
If a 4K version is released on physical media, then that may not (immediately) apply to streaming services. The releasing studios should upload their 4K release to the Store owner, in this case to Apple. Users will have to wait until that happens.
If a movie property is now in different hands than any previous HD version, then the upgrade may not happen automatically. It should work most of the time, but there may be exceptions.
HD vs. 4K availability may also differ by market region (country or country-like region). So please disclose the country to which your Apple Account is set.
Apple TV HD, tvOS 18
The Apple TV HD [A1625] (2015) will never display 4K content. The hardware is limited to HD output max. You’ll need to use a modern Apple TV 4K box, or a 4K smart TVs built-in Apple TV app, or a supported third party streaming device, to watch Apple’s iTunes Store 4K content in 4K.