How do I create a Local html file to open webpage and inject a JavaScript function

I have a legacy web application that we are not allowed to modify yet. We need to add a new function to the application in the short term. We have been told that we may modify the webpage with any local scripts we want but we have to wait 4 months before they will unlock the application.

So my goal is to create a webpage locally, click on that local html file and have it open the url for the legacy application, and then inject the new JavaScript function to the application.