Hi @littledevil
You need to get the repeater first before updating it. I think something like this:
$booklink = $_POST['booklink'];
$field_key = "books";
$value = get_field($field_key, $post_id);
$value[] = array("booklink" => $booklink );
update_field( $field_key, $value, $post_id );
I hope this helps.