Search result page as a new page

You can use custom template for search page:

<?php


 get_header(); ?>

    <section id="primary" class="content-area">
        <div id="content" class="site-content" role="main">

        <?php if ( have_posts() ) : ?>

            <header class="page-header">
                <h1 class="page-title"><?php printf( __( 'Search Results for: %s', 'shape' ), '<span>' . get_search_query() . '</span>' ); ?></h1>
            </header><!-- .page-header -->

            <?php shape_content_nav( 'nav-above' ); ?>

            <?php /* Start the Loop */ ?>
            <?php while ( have_posts() ) : the_post(); ?>

                <?php get_template_part( 'content', 'search' ); ?>

            <?php endwhile; ?>

            <?php shape_content_nav( 'nav-below' ); ?>

        <?php else : ?>

            <?php get_template_part( 'no-results', 'search' ); ?>

        <?php endif; ?>

        </div><!-- #content .site-content -->
    </section><!-- #primary .content-area -->