I am just wondering if there is any hook to integrate WHMCS database with my existing Drupal site.
WHMCS has its own CMS and so as Drupal. I have used the same html twice for WHM and also for Drupal hence the problem is that I have to change twice if there is any design update.
The answer is no, there is no such thing.
A hook, in Drupal is not something magically to integrate anything. A hook is merely a architectual concept to allow code being ran on several occasions. A hook is not what you are looking for.
You will need to implement each and every piece of integration with Create, Read, Update, Delete synchronisation. A user in Drupal gets updated, that should fire code wich updates the data in your other CMS's database. A piece of content is created in your WHCMS, then it needs to become available in Drupal too. And so on and so on.
So, you will first need to define very clearly what you want to integrate and share between both. If it is only the session (single sign on) there are several solutions ready to use. But if you need all content, their comments, search-results and so on to be shared, you have a long way to go.
The reailty with integrating two CMS's entirely, is that you often need more then the sum of the codebase of both CMSs as gluecode: it needs such great amounts of complex integration and synchronisation-code, that in the same time you had probably written both Drupal and WHCMS from ground up. My advice: don't even try.