Ah. So, I would be on a page that has the search form, and a list of posts. In those posts are the authors. You want to be able to click the author, and instead of going to the author page, you want to trigger the search and add that author?
So, the author field would need to be in the form. Would you want to show it or hide it? If you want to hide it, use some custom CSS to do that, but, if you hide it, how does the user remove it from the search if they want to?
The Author term would have to be a link that triggers some custom JavaScript to run.
That would fetch the term from the link, set that in the form field, and then trigger a submit, using
$('.searchandfilter').submit()