The option for this is available when you are inserting a custom search View into a page.
When you insert a View with the Fields and Views button the resulting dialog will ask whether you want to insert the search form and results, or to insert just the search form and insert the results separately.
The GUI guides you through what's required, it should be fairly straightforward, but if you can't do it for some reason then let me know.
I know where this is when setting up a 'new' search, just wondering of this was able to be done to an existing one where the results are currently on the same page.
Guess I can remake the search again taking into account this. Worth an ask.
You don't need to make a new View, you just need to insert the View again. So wherever you currently have it (inserted with a wpv-view shortcode), delete that and insert it again using the Fields and Views button.