Retrieve Custom Taxonomies according to posts selected

The loop for $listings should include a call to $listings->the_post() so that the global post object is assigned to the current listing in the loop:

        while ( $listings->have_posts() ) {
            /*** Add the following line: ***/
            $listings->the_post();

            $post_get = get_the_ID();
            $term_get = get_the_terms($post_get, 'Car_Series');
            $term_array = $term_get;
            print_r($term_get);
            array_push( $term_array, $term_get);
        }

Without this, functions that rely on the global post object, such as get_the_ID() will not return the expected results.