Assign a class to a child if condition is true

Assign a class to a child if condition is true

How would I go about giving a child element a class if the parent element
contained style="display: none;" and a certain class?
For example, I want:
<div style="display: none;" class="hidden">
<a href="#">Hidden</a>
</div>
to be:
<div style="display: none;" class="hidden">
<a href="#" class="new-class">Hidden</a>
</div>