This appears to work:

editor.keyboard.bindings[9].unshift({
key: 9,
handler: function(range) {
console.log('user hit tab');
return true;
}
});

It appears as though a pre-existing handler runs first and prevents my handler from running. Is there a way to put my handler first?

Yes. You can overwrite the default binding, problem is you can't do with addBinding() but only with configuration just like this docs example: Keyboard Module configuration

@DmitrySkripkin When I use the example you pointed to it prevents the tab character from appearing in the quill editor or it prevents anything from happening at all, depending on whether I return true or not. Is there a way to get the default behavior, where the tab appears in the editor, but my code also runs?

I dig a bit deeper. Default tab handler does not return anything. So even if you add a new binding it won't be executed anyway.

This means you have to rewrite it - basically copy/paste it or use method with unshift() you mentioned above.

P.S. Quill is not perfect, I would like to have more flexible bindings with some kind of weights to sort them.

The problem is key has to be a number... It's even against type declared in @types/quill

Quill 2.0 has been released (announcement post) with many changes and fixes. If this is still an issue please create a new issue after reviewing our updated Contributing guide 🙏