Reload wordpress shortcodes

If you want to do this via AJAX, on the server side you could do something like the following:

add_action( 'wp_ajax_nopriv_update_shortcode_content', 'update_shortcode_content' );

function update_shortcode_content(){
    if( !empty( $_GET['new_shortcode_value'] ) ){
        $updated_content = do_shortcode( '[theshortcode value="' . $_GET['new_shortcode_value'] . '"]' );
        wp_send_json( array( "content" => $updated_content ) );
    }
}