Nothing. Unfortunately, Live tiles are basically only a way to start the application, but even though the appearance of the live tile can change, the shortcut can't. It is up to the app to properly support it.
The problem you're facing is that the live tile shows what's on the front page (aka, when you open the app), except that the live tile doesn't update as frequently as the news on the front page does. So basically you see older news and as such when you click you have to search for that article. Its usually not that far away but chances are slim you will actually land on the actual article.
So there's basically nothing you can do. Maybe find a way to update the live tiles more quickly, but I'm not sure that's what you want anyway.
Live tiles are a fun feature, but you should basically open the app, read all the news then close it again, and leave the live tile for what it is, a quick way to see where your news app is.
ah, undertand.. oh well maybe they will add an API in a few years and apps can support that – Mikey – 2017-01-26T09:05:36.157
is there any way to increase the frequency of the updates? The weather app is only semi-live for me... Often a few degrees off from the "click-through" – Mikey – 2017-01-30T02:54:54.920
@Mikey apparently not. See: http://superuser.com/questions/498602/change-duration-of-live-update-in-metro-ui-apps-windows-8
– LPChip – 2017-01-30T07:39:18.540