It’s not an out-of-the-box feature that is possible. 

However, I’ve created versions of this for bringing certain tags into dedicated slack channels. 

You can automate based on available webhooks via the API (or pre-built triggers if you use Zapier) for new questions. From there, your automation will need filter conditions based on the tags (which are in the data payload). If the tag you’re looking for is included, you can automate the action like a slack message or something else. 

There is an open idea for this (I voted for it a few months ago). It’s quite a popular request!

Thank you @DannyPancratz for sharing the workaround. This is very helpful.

@lwackertn thank you for the sharing the open idea link. Looks like the Idea is sitting there from past 3 Year