Im trying to add a div for just one category

by

To wrap the thumbnail wit I would do something like this:

First. Create the expire class string

$expire_class = in_category('expired') ? 'expire' : '';

Then, wrap your post thumbnail code with this:

<div class="<?php echo $expire_class; ?>" > 
[put your thumbnail code here]
</div>

So, it looks like this:

<?php
$expire_class = in_category('expired') ? 'expire' : '';
if(has_post_thumbnail())  {
        ?><a href="https://wordpress.stackexchange.com/questions/288469/<?php the_permalink(); ?>"><div class="<?php echo $expire_class; ?>" > <?php the_post_thumbnail(
            array($theme->get_option('featured_image_width'), $theme->get_option('featured_image_height')),
            array("class" => $theme->get_option('featured_image_position') . " featured_image")
        ); ?></div></a><?php  
    }
?>