Add class when more page is visited

It seems you are looking for body_class()

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A solution for adding a body class to a specific page template:

add_filter( 'body_class', 'custom_class' );
function custom_class( $classes ) {
if ( is_page_template( 'page-example.php' ) ) {
    $classes[] = 'example';
}
return $classes;
}

The result on the front-end:

<body class="page page-id-7 page-template page-template-page-example page-template-page-example-php example">