It works for me by using require syntax like this:
$('.eventSlick').slick({
dots: true,
slidesToShow: 3,
slidesToScroll: 1,
autoplay: false,
autoplaySpeed: 2000,
arrows: true,
draggable: false,
prevArrow: '<button type="button" data-role="none" class="slick-prev"><img src="' + require("@/assets/img/icon/Arrow_Left.svg")+'"></button>',