Answer by Pete L. Clark for Adding a short (and interesting) observation to a submitted paper

I can add it to my old paper and resubmit it, but even if it's not too late to do so, I'm afraid that my result won't get noticed (as the long paper will only attract a small number of specialists)

It is certainly not too late to do so -- you haven't even received a first referee report yet. I suggest that you add the extension of the old, classical result to the present paper. There are two aspects here:

Rewriting the paper:

If you just tack the new result / proof on at the end of a long paper, indeed it might not get noticed. So don't do that. Rewrite the abstract and introduction of the paper so that your new result / proof gets much more prominence: if the deduction is only a paragraph, you could even do that in the introduction. This is a great way of selling the results of a long, technical paper!

Resubmitting the paper:

You could either send a new version of the paper to the editor and ask them to send it to the referee or you could wait for a referee report. In my opinion, either one should probably work here: the changes are not going to bother the referee, and if the paper gets accepted, neither the editor nor the referee is going to be bothered by a new version with the same technical guts but with superficial rewriting so as to permit a nice new application. What I would say is: since you know how to improve your paper and it hasn't been accepted yet, the smartest move seems to be giving the referee access to the improved version before they make up their mind...if the editor is on board with that.

So: I would suggest writing a new version, sending it to the editor, and seeing what they think.