$(function(){
if($('.slick-active').data("slick-index") === "2"){
$('.new_class').css("display", "block");
}
});
<div class="slick-slide slick-current slick-active" data-slick-index="2" aria-describedby="slick-slide02">
<div class="new_class" style="display:none;">тест</div>
</div>