You need to think about where the code is running at different times. Your JSP is a servlet, it runs on the server and sends HTML to browser. Once the browser has rendered the HTML page your JSP is no longer running, you've just got HTML in the browser.
That page may have links, or Form submit buttons which will invoke a new resource such as a servlet or JSP on the server and get a whole new page back to the browser. I don't fully understand your question, I think you don't want to POST a form, but you could just allow the user to click on a link.
However, I suspect that what you want to do is update part of the page without redrawing the whole thing. This is sometimes called AJAX programming. Some JavaScript in your HTML page runs, makes calls to the server and then modifies the HTML, hence displaying new data.
AJAX is a big topic, needs JavaScript skills and greatly benefits from a framework such as Dojo or JQuery. I suggest that you google your way around these subjects a bit and then come back with specific questions.