Thank you John. I hadn’t realised that it was updating to a post and not the taxonomy. Thank you for all your help!

Sorry I was trying to keep the code simple to post on here. Yes, sorry I understand that the $value
will always be 8. This value eventually be drawn from a mysql query so will show between 1 – 10 depending on the result.
What I have is a custom taxonomy field which I wanted to store the average review score of all the customer reviews related to that taxonomy. So for example if the company’s average score was 8 then it would update my average_review_score field. I can then draw on this value for other parts of the site. This will be updated whenever I call a function that I have written.
In the function it draws the data via a mysql query. From what I understand I then need to use update_field( $field_key, $value, $post_id );
to update the field. This appears to work because if I execute the following code
$get_av = get_field( "average_review_score", $post_id );
echo $get_av;
it has changed the value to whatever I enter.
However when I view the Edit Tag in wp-admin its still showing the old value that I originally entered:

I must admit I might have totally misunderstood what I can and cannot do when updating the field. But I basically want to update the value, both in the frontend and backend of the site.
Hopefully this makes it a little clearer as to what I’m trying to accomplish.