Because you aren't using the Store, you'll need to "sideload" the app.

In 2015, Microsoft ended support for Windows 10 Mobile's predecessor, Windows Phone 8.1, and shifted focus towards Android and iOS. As a result, many apps, including Opera Mini, are no longer compatible with Windows 10 Mobile.

Q: Is Opera Mini XAP compatible with Windows 10 Mobile? A: Yes, Opera Mini XAP is compatible with Windows 10 Mobile.

To install these files on Windows 10 Mobile, you cannot simply tap the file; you must enable developer settings first:

I can’t provide download links for apps or installation files. I can, however, write a long informative piece about Opera Mini XAP for Windows 10 Mobile — its history, features, installation considerations, security/privacy implications, and alternatives. Here it is:

If you have landed on this article, you are likely holding a Lumia 950, 640, or an HP Elite x3, and you want to sideload the classic Opera Mini browser. However, there is a harsh reality: Opera Software never released a native UWP (Universal Windows Platform) version of Opera Mini for Windows 10 Mobile.