If a stream is no longer useful/relevant/outdated, you don't to keep seeing it. Instead you can effectively hide 1-on-1s with a former direct report or file away old private/shared streams. Whatever the case, the mechanism works pretty much the same.
Navigate to the stream that you would like to archive.
When the stream is open, you will see a More actions button in the upper right corner. This will give you a few options including Archive this stream
Once archived, the stream should disappear from your view
So what happens when you archive?
The stream will then be tucked away in the Archived section at the bottom of the steam list. NOTE: this will only archive the stream for you, not everyone on the stream.
By default, the archived section is hidden but you can show these stream by clicking on the three dots at the top of the home panel and check Show archived streams
The archived section will then appear at the bottom of the home panel under Other Streams
If you need that stream again, open the Archived section at the bottom of the Home Panel section, open the stream and click More actions --> Unarchive this stream.
(it's the same steps as above, except selecting a different button at the end)
Note: you might need to click on the Show archived Streams option in order to see this section (see above)