WordPress custom taxonomies new/edit post autocomplete

As far as I remember WP core doesn’t do this natively, though I think there are/were some considerations about adding select2 for tasks like this. Might be mistaken on this.

However there are a lot of frameworks around, which implement additional UI for things like this. It’s pretty common feature in them. I tend to use Meta Box, which should be able to do it, but so can others.