It is by design that the link you distribute points to the last published version. So, since you haven't published the new version it is not being shown. If you want the link to redirect to the new version, you will have to publish it.
Are you trying to do some sort of preview with just a few insider users to test that everything works before broadly publishing? We don't have a built-in way of doing that directly that I'm aware of. I guess a workaround would be to Save As the app and publish that new app -- sharing it with just the few target users. So, the new app copy would be a preview which you could later delete. Not too elegant, but it might solve the problem.
That being said, having a preview/insider sort of thing for PowerApps could be helpful. So if you're looking for something like that, feel free to share an idea in the Ideas forum.