function create_nonce() {
    return wp_create_nonce('my-nonce');
}

add_action('wp_ajax_create_nonce', 'create_nonce');
add_action('wp_ajax_nopriv_create_nonce', 'create_nonce');

$('form').on('submit', function(e){
    e.preventDefault();
    var $form = $(this);

    request('create_nonce', function(nonce){
         // Append the fresh nonce to the form
         $form.append('<input type="hidden" name="nonce" value="'+nonce+'">');

         // Proceed with the form submission...
    });
});