Notify new post on page

You can use the publish_post action, which is triggered when a post is published. Knowing that, you can create a function and call that function whenever the publish_post action is triggered using the add_action function.

An example from the docs:

function post_published_notification( $ID, $post ) {
    $author = $post->post_author; /* Post author ID. */
    $name = get_the_author_meta( 'display_name', $author );
    $email = get_the_author_meta( 'user_email', $author );
    $title = $post->post_title;
    $permalink = get_permalink( $ID );
    $edit = get_edit_post_link( $author, '' );
    $to[] = sprintf( '%s <%s>', $name, $email );
    $subject = sprintf( 'Published: %s', $title );
    $message = sprintf ('Congratulations, %s! Your article “%s” has been published.' . "\n\n", $name, $title );
    $message .= sprintf( 'View: %s', $permalink );
    $headers[] = '';
    wp_mail( $to, $subject, $message, $headers );
}

add_action( 'publish_post', 'post_published_notification', 10, 2 );