To change the vehicle category permalink slug, add the below code in the child theme’s functions.php.

add_filter( 'cdhl_cars_taxonomy_vehicle_cat', 'cardealer_child_extend_taxonomy_vehicle_cat' );
function cardealer_child_extend_taxonomy_vehicle_cat( $args ) {
	$args['rewrite']['slug'] = 'vehicle-cat';
	// The above code will change the vehicle category slug from "vehicle-category" to "vehicle-cat".
	// You can change it as per your requirements.
	return $args;
}

You can adjust the code as per your requirements.