How to avoid duplicate sticky post in home page?

The intention of the slider is to bring older content to the front page. Excluding individual posts from the loop is a process I don’t personally recommend, you can simply mark it sticky after it’s pushed away from the home page.

However if you wish to exclude them, you can go to functions.php, function esplanade_ignore_sticky_posts and replace the line

$query->set( 'ignore_sticky_posts', 1 );

with

$query->set( 'post__not_in', get_option( 'sticky_posts' ) );