Count Number of Posts in Taxonomy Term in Last 24 Hours

You can create a custom WP_Query and count its result.

$wp_query = new WP_Query([
    'tax_query' => [
        [
            'taxonomy' => 'news',
            'terms' => $term_name,
            'fields' => 'name'
        ]
    ],
    'date_query' => [
        [
            'after' => '24 hours ago'
        ]
    ]
]);
$number_of_posts = $wp_query->found_posts;

Edit

I removed posts_per_page argument, as @birgire suggests, that found_posts offers total number of posts regardless of pagination.