Hi,
That entirely depends on your theme. Firs try this option, quality themes use the get_search_form() feature, which allows replacing the search forms automatically. If there was a search bar originally on the results page, then this should do the trick.
If no luck, then check your theme settings. A lot of themes now have visual builders, which let you replace certain blocks. With that you can place the search shortcode there.
If that is not an option, then try asking the theme author first – usually there is either a different way or just a simple file modification to place the plugin shortcode to the results page.