code: protected void displayArrowForAllowClearOption(boolean displayArrow) {
          if (isAllowClear()) {
              if (displayArrow && getArrowIconElement() != null) {
                  getArrowIconElement().css("display", "block");
              } else {
                  getArrowIconElement().css("display", "none");
              }
          }
      }
docs: Will automatically check for allowClear option to display / hide the
  arrow caret.