I think you need to supply more information or try to help yourself finding hooks in the WordPress codex.
To help you along, regarding a hook on a new post insertion, you can use ‘wp_insert_post’:
function wp_insert_post_hook( $post_ID, $post, $update )
{
$some_condition = true;
if ( $some_condition )
wp_delete_post( $post_ID );
}
add_action( 'wp_insert_post', 'wp_insert_post_hook', 10, 3 );