get_header
has an action hook called, (surprise!) get_header
which gets a single parameter – the name of the header file. So what we do is check that name and if it matches our name we add a style. So something like this:
add_action( 'get_header', 'wpse_260353_add_css_for_header' );
function wpse_260353_add_css_for_header( $name ){
if( 'modern' === $name ){
wp_enqueue_style('landing-style', get_template_directory_uri() . '/css/navbar.css');
}
}