/**
 * Add custom badge to WooCommerce products in a specific category.
 */
function wpsimpel_add_category_product_badge() {

    if( has_term( 'posters', 'product_cat' ) {
        echo '<span class="product-badge custom-badge">' . esc_html_e( 'New arrival', 'your-text-domain' ) . '</span>';
    }
}
add_action( 'woocommerce_before_shop_loop_item_title', 'wpsimpel_add_category_product_badge' );
add_action( 'woocommerce_before_single_product_summary', 'wpsimpel_add_category_product_badge' );