Every theme (almost all...) come with a snippet of code that renders a single product. A theme will use that snippet of code to render a product in a collection of products. So the first thing you do, is inspect your collection Liquid templates for the product template that they use to render a product.

Now you can edit the product template. While there are many elegant ways to do this, I will give you the basic bush league level one.

{% if collection.handle == 'some-dumb-collection' %}
   {% comment %}
   {{ someproduct_variant.price }}
   {% endcomment %}
{% endif %}

In other words... if we are in that special collection, comment out or hide the price.

You can definitely use that pseudo code to help you along.