$('.slider').on('click', '.slick-current', function() {
$(this).addClass('clicked-current-slide');
});$(document).ready(function(){
$('.slick-slider').slick();
});
<div class="slick-slider MYSTYLECLASS">
<div class="MYSTYLECLASS__ITEM">your content</div>
<div class="MYSTYLECLASS__ITEM">your content</div>
<div class="MYSTYLECLASS__ITEM">your content</div>
</div>
<div class="slick-slider MYSTYLECLASS-2">
<div class="MYSTYLECLASS-2__ITEM">your content</div>
<div class="MYSTYLECLASS-2__ITEM">your content</div>
<div class="MYSTYLECLASS-2__ITEM">your content</div>
</div><div class="slick-slide"><div class="container-content">слайд 1</div></div>
<div class="slick-slide slick-current"><div class="container-content">слайд 2</div></div>
<div class="slick-slide"><div class="container-content">слайд 3</div></div>.slick-current > .container-content {
transform: scale(2);
}// в них добавляешь что то типо того
appendDots: $(this).closest('.slider').find('.SlickNavBlock'),
appendArrows: $(this).closest('.slider').find('.SlickNavBlock'),prevArrow: '<span class="slick-arrow_custom-left"></span>',
nextArrow: '<span class="slick-arrow_custom-rigth"></span>',
dotsClass: 'slick-custom-dots',