need to exclude APP_TAX_STORE => $term->slug

The easiest way I can see is to gather a list of the terms in that taxonomy, and use them with a NOT IN operator in your query’s tax_query:

// Get all the terms in your custom taxonomy.
$slugs = get_terms( [
    'taxonomy' => 'industry',
    'fields'   => 'slugs',
] );

$posts = query_posts( [
    'post_type'      => 'post',
    'posts_per_page' => 4,
    'post_status'    => 'publish',
    'tax_query'      => [
        [
            'taxonomy' => APP_TAX_STORE,
            'operator' => 'NOT IN',
            'field'    => 'slug',
            'terms'    => $slugs, 
        ]
    ]
] );

I would suggest reading up on query_posts if you haven’t already – heed the warning that it could cause confusion and trouble down the road. get_posts should get you the same results without the burden of overwriting the main query.