Where this code is in what you shared
$description = filter_input( INPUT_POST, 'description', FILTER_SANITIZE_STRING );
// removing action to avoid recursion
emove_action( current_filter(), __FUNCTION__ );
wp_update_term( $term_id, $the_target_tax, array( 'description' => $description ) );
You need to get the value of the field and then use the following to update the field
update_field($field_key, $value, 'term_'.$term_id);