Get Term ID by Description

I’m not aware of ready-made functions that support this, but you can easily construct a WP_Term_Query to do this. The following code is untested but should work:

$args = [
    'description__like' => 'the description you\'re searching for',
    'taxonomy'          => 'category',//or other taxonomy
    'fields'            => 'ids',
    'hide_empty'        => false,
];
$term_query = new WP_Term_Query($args);
foreach ($term_query->terms as $term) {
    // ID is in $term->term_id
}