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(); ?>