The solution is very simple. In template.php file implement `MY_THEME_preprocess_node()`. Example:

    function MY_THEME_preprocess_node(&$variables) {
      //  dpm($variables);
      if($variables['type'] == 'MY_CONTENT_TYPE') {
        $date_field_value = $variables['content']['field_DATE_FIEL_NAME'][0]['value']; // find the correct value of your field
    
        $converted_date = strtotime($date_field_value);
    
        if(time() > $converted_date) {
          hide($variables['content']['field_DATE_FIEL_NAME']);
        }
      }
    }

you can also use `hook_node_view`:

    function MY_MODULE_node_view($node, $view_mode, $langcode) {
      if($node->type == 'MY_CONTENT_TYPE') {
        $date_field_value = $node->content['field_DATE_FIEL_NAME'][0]['value'];
    
        $converted_date = strtotime($date_field_value);
    
        if(time() > $converted_date) {
          hide($node->content['field_DATE_FIEL_NAME']);
        }
      }
    }