ACF add custom fields to categories and display

Check this page out from the ACF docs: https://www.advancedcustomfields.com/resources/get-values-from-a-taxonomy-term/

Specifically this section:

“Finding the term related to the current post”

<?php

// load all 'category' terms for the post
$terms = get_the_terms( get_the_ID(), 'category');


// we will use the first term to load ACF data from
if( !empty($terms) ) {

    $term = array_pop($terms);

    $custom_field = get_field('header_image', $term );

    // do something with $custom_field
}

?>

I changed their “category_image” to your “header_image” value. I think that should work for you.