The best way is you should destroy the slick slider after reinitializing it.
function slickCarousel() {
$('.skills_section').slick({
infinite: true,
slidesToShow: 3,
slidesToScroll: 1
});
}
function destroyCarousel() {
if ($('.skills_section').hasClass('slick-initialized')) {
$('.skills_section').slick('destroy');
}
}
$.ajax({
type: 'get',
url: '/public/index',
dataType: 'script',
data: data_send,
success: function() {
destroyCarousel()
slickCarousel();
}
});