This gets the terms:
$terms = get_the_terms( get_the_ID(), 'nieuwssoort');
Then you check the result:
$terms_ids = [];//you can set a default id here
if(false !== $terms && !is_wp_error($terms)){
foreach($terms as $term){
$terms_ids[] = $term->term_id;
}
}
We check the result just in case.
Now, we have the values, let get them into the arguments:
$args = array(
'post_type' => 'nieuws',
'orderby' => 'date',
'post__not_in' => array($currentID),
'tax_query' => array(
array(
'taxonomy' => 'nieuwssoort',
'terms' => $terms_ids
),
),
'posts_per_page' => '7',
);
I can’t test the code right now, but I think it should work.