hello,
yes, you can remove the search option on the header. you can go to header.php and remove or close search function.
like
<div class=”search-toggle”>
<?php _e( ‘Search’, ‘twentyfourteen’ ); ?>
</div>
<nav id=”primary-navigation” class=”site-navigation primary-navigation” role=”navigation”>
<button class=”menu-toggle”><?php _e( ‘Primary Menu’, ‘twentyfourteen’ ); ?></button>
<?php _e( ‘Skip to content’, ‘twentyfourteen’ ); ?>
<?php wp_nav_menu( array( ‘theme_location’ => ‘primary’, ‘menu_class’ => ‘nav-menu’ ) ); ?>
</nav>
</div>
<div id=”search-container” class=”search-box-wrapper hide”>
<div class=”search-box”>
<?php get_search_form(); ?>
</div>