How call WordPress shortcode inside function file

I need echo do_shortcode('[Shortcode]'); to go where it says “New
Item Contents here!” is there any way to do this?

Just put it there:

add_action( 'woocommerce_account_new-item_endpoint', 'add_new_item_content' );

/**
 * Add content to the new tab.
 *
 * @return  string.
 */
function add_new_item_content() {
    echo do_shortcode('[Shortcode]');
}

Maybe I’m misunderstanding the question, but that’s all you need to do.