condition for specific pages

The easiest way to do it would be:

if ( is_category ('4') ) {
 echo '<a class="btn" href="">Enquire</a>';
} else {
 echo '<a class="btn" href="">Calendly link</a>';
}

Obviously you would change “4” to whatever the specific category number is.

Also, the WordPress template hierarchy could be helpful if you have add’l changes:

https://developer.wordpress.org/themes/basics/template-hierarchy/#category

Graphical view of the Template Hierarchy

If you want a special template for the category 4, you just save the template file as category-4.php in your child theme folder.