displaying a fall back query if there’s nothing in the post-type category

In this situation get the term of post,and then calculate number of posts in it.
make a if condition for checking, posts in that term is zero or greater then zero then $args for WP_query.

<?php 
    global $post;
    $term = get_term( 'hometwo', 'Presenter-type' );
    $posts_in_term = $term->count;
?>
<?php
if($posts_in_term > 0 ){
    $args = array(
            'post_type' => 'presenters',
            'posts_per_page' => 1,
            'tax_query' => array(
                array (
                    'taxonomy' => 'Presenter-type',
                    'field' => 'slug',
                    'terms' => 'hometwo'
                )
        )
    );
}
else{
    $args = array() //your default query;
}

$query = new WP_Query ( $args );
?>
<?php if ($query->have_posts()) : ?>
<?php while ($query->have_posts()) : $query->the_post(); ?>
    <a href="https://wordpress.stackexchange.com/questions/99798/<?php the_permalink(); ?>">
    <?php the_post_thumbnail(); ?>
    <h3><?php the_title(); ?></h3>
    <p><?php the_excerpt(); ?></p></a>
    <?php endwhile; ?>
    <?php else : ?>
<?php endif; ?>
<?php wp_reset_query(); ?>