In order to do this, you will need to override the default page with custom VisualForce, include the default layout, and then write a custom component that only lists active contacts.
Another option would be to just configure the contact related list on the Account page to be sorted by active status. This would push the inactive contacts to the bottom and would save you some headache of writing custom code.
Another option would be to just configure the contact related list on the Account page to be sorted by active status. This would push the inactive contacts to the bottom and would save you some headache of writing custom code.