You could try this code on your child-theme’s functions.php
add_action( 'frontier_after_top_bar', 'ra_search_on_top' );
function ra_search_on_top() {
?>
<form id="top-bar-search" action="<?php echo home_url( '/' ); ?>" method="get" role="search" style="float: right;">
<input type="search" name="s">
<input type="submit" value="Search">
</form>
<?php
}