How to upgrade Apple Pages?

Apple does not maintain user downloadable versions of its past, full installers. Presently, the Mac App Store requires that you are running Catalina 10.15.n, or Big Sur 11.n.n for installation of Pages v10.3.9 (current). The last version of Pages for Mojave is v10.1, and if you have that, you are done.

If you have a version of Pages older than v10.1 on Mojave, there is a (slim) possibility that you could get it updated through the Mac App Store, provided that you sign-in with the same Apple ID used to install it previously. With the Mac App Store launched, press ⌘+0 (zero). That takes you to the previous purchase page, where you can click on the Pages icon if it offers an Update button or a blue cloud with a download symbol.

It will pop a dialog telling you that you cannot install the current version of Pages from the Mac App Store but might show you a second dialog that offers to update your version of Pages to v10.1. Do not be surprised if you do not get that secondary dialog.

Although Apple does have a three-year sliding window of support for operating systems, that does not extend to past application installers. Been this way for years, and Apple is not infallible.