When done properly, external style sheets can be kept to a minimum size, removing the urgency for them to be placed in browser cache. However, if you are using a caching system or CDN, that can be difficult to overcome.

In the following, we use a time code when enqueueing the style sheet, which will overcome caching because our functions.php document will always be looking for the document saved with the specified time code, which should include our lastest changes.

Place the following code anywhere in your child theme’s functions.php document. I prefer to place style sheets and external scripts first thing in the document, after the opening block of information describing the functions.php document.

// register child styles with a time code (to overcome cache)
function my_important_styles() {
    wp_enqueue_style('custom-styles',
    get_stylesheet_directory_uri() . '/style.css',
    array(), filemtime(get_stylesheet_directory() . '/style.css'), false);
}
add_action('wp_enqueue_scripts', 'my_important_styles', '999');