Link to post author but exclude administrator (on single.php)

by

You can use the wordpress function user_can that accepts as arguments the id of the user and a string representing a capability or a role name (‘administrator’ in your case ) and returns a boolean value.

http://codex.wordpress.org/Function_Reference/user_can

Referred to your code you can try this

<?php 
  if( !user_can( get_the_author_meta( 'ID' ), 'administrator' ) ): ?> 
    <a href="https://wordpress.stackexchange.com/questions/173503/<?php echo get_author_posts_url( get_the_author_meta("ID' ) ); ?>" ><?php the_author_meta( 'display_name' ); ?></a>
<?php 
  endif; ?>