The Chrome team at Google is working on a new feature that they call “Media Sessions” which will let Chrome pause media currently playing when you play something on another tab.
The plan here is to set a default audio focus which will change based on which tab the user is. For example, in the video linked above, you will see music playing on one tab. As soon as the second tab starts playing a YouTube video, the first tab stops playing music.
A future enhancement to this might include the paused tab automatically resuming playback when the newly opened tab with media is closed.
This feature is currently under development. This might take a while before it shows up on Chrome. It might even have a different name when it becomes the final product.
If you are a developer who wants to explore details about this, find the commit log here.