As soon as your YouTube live stream ends, YouTube will automatically save an archive of it to your channel. You can download your previous live streams the same way you can download previously uploaded videos. Here’s how to do it:
Go to studio.youtube.com and make sure you’re signed into the right channel.
Click Content on the right side of the studio dashboard.
Click the Live tab under Channel Content.
Your previous live streams will appear in the list under Live.
Hover over the live stream you want to download and click the three dots.
From the options that appear, click Download.
Note: You can only download live streams from your channel; you cannot download someone else’s previous YouTube Live broadcasts. Also, YouTube only archives live streams under 12 hours long.