I think I understand what you mean.
On the front end of the site, when the post is displayed, either the full article or the excerpt, you only want the selected tags to be shown for that post.
These are usually shown using the function get_tag_list() https://codex.wordpress.org/Function_Reference/get_the_tag_list
There is no easy way to filter what this outputs.
Basically, what you’re going to need to do is replace this function. You can can create a filter
add_filter('the_tags', 'my_replace_tags');
function my_replace_tags($html) {
// generate your own html for only the tags you want to show
$html = ????
return $html;
}
