You can concatenate two transitions or more, and visibility is what comes handy this time.

div {
  border: 1px solid #eee;
}
div > ul {
  visibility: hidden;
  opacity: 0;
  transition: visibility 0s, opacity 0.5s linear;
}
div:hover > ul {
  visibility: visible;
  opacity: 1;
}

<div>
  <ul>
    <li>Item 1</li>
    <li>Item 2</li>
    <li>Item 3</li>
  </ul>
</div>

(Don't forget the vendor prefixes to the transition property.)

More details are in this article.