First, upgrade to the latest version of Zotero. You're still on 3.0.8.1.

Next, if it's still slow, provide a Debug ID for tagging one item. It'd be useful to have one Debug ID with the tag selector closed and another with it open. (You can drag the divider above it down to close it.)

Is most of the delay with typing the tag or after you press Return?

It looks like you have a very large number of tags, so I suspect you'd see a big improvement in speed when tagging items with the tag selector closed. If you look at the gray divider above it, below the collections list, you should see a little dot in the center. You should be able to close the tag selector by either clicking and dragging that dot or just by clicking it once.

Closing the tag selector won't help with any delay while typing tags. That'd be due to auto-complete, which may also be slow with a huge number of tags, but we could increase the delay for libraries with a large number of tags to allow you to keep typing without the interruption.

We'll see what we can do to speed up the tag selector for libraries like yours.

The delay occurs after pressing add i..e adding the tag.

(Just so you know, clicking "Add" actually just shows a new empty tag entry box—there's no need to click that to save a tag. You can just press Return when you're done typing and you'll get another empty entry box, which should be faster for entering multiple tags. (You can also click anywhere else in the interface and it'll have the same effect as clicking that button, since the tag is just saved when the entry box loses focus.))

I have now closed that divider and that did improve the speed pf tagging, although I still have to wait a few seconds after pressing add or clicking on the next item

OK. The performance you're seeing with the tag selector closed is unfortunately probably the best you'll see for now with that many tags, but we'll see what we can do to speed things up in future releases.

Thank you very much for clarifying this! After closing the tag area it's now several orders of magnitude quicker (i.e. basically instantly instead of taking 30 seconds). This has really been driving me mad! Thank you for your valuable work!