Advanced Custom Fields query

I think this should work, but I am not 100% certain on the advanced meta query for “not” a null string. That isn’t normally how meta queries are used. As such, I have left the set_transient line commented out. I just noticed that you are trying to pull 1 random post, so you might not want to use the Transients API at all, but I think it would still be a good idea just with a shorter time limit, so I have the transient set to store for 1 hour. If not, you can always extract the query parts.

// Get any existing copy of our transient data
if ( false === ( $custom_testimonials = get_transient( 'custom_testimonials' ) ) ) {
    // It wasn't there, so regenerate the data and save the transient

   // params for our query

   array(); ?


    $args = array(
        'post_type' => 'our-clients-list'
       'posts_per_page'  => 1,
       'orderby' => 'rand'
       'meta_key'        => '_featured',
       'meta_value'      => 'yes',
        'meta_query' => array(
            array(
                'key' => 'testimonial_',
                'value' => '',
                'compare' => '!='
            )
        )
    );

    // The Query
    $custom_testimonials = new WP_Query( $args );

    // store the transient - uncomment when sure the query is working (stores for 1 hour)
    // set_transient( 'custom_testimonials', $custom_testimonials, 60*60*1 );

}

// Use the data like you would have normally...

// The Loop
if ( $custom_testimonials ) :

    echo '<ul class="testimonial">';

    while ( $custom_testimonials->have_posts() ) :
        $custom_testimonials->the_post();
        echo '<li>' . get_the_title() . '</li>';
    endwhile;

    echo '</ul>';

else :

echo 'No testimonials found.';

endif;

/* Restore original Post Data
 * NB: Because we are using new WP_Query we aren't stomping on the
 * original $wp_query and it does not need to be reset.
*/
wp_reset_postdata();

Excellent reference on Advanced Meta Queries