JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="//cdn.jsdelivr.net/npm/[email protected]/slick/slick.css">
<script src="//cdn.jsdelivr.net/npm/[email protected]/slick/slick.min.js"></script>
<div class="slider">
  <div>1</div>
</div>
<button>Добавить</button>

JavaScript

$('.slider').slick({
  infinite: true,
  slidesToShow: 3,
  slidesToScroll: 3
});

$('button').on('click', function() {
  $('.slider').slick('slickAdd','<div>0</div>', 0, true);
});