Yes, you certainly can add your Clients' Tax Numbers or VATs on your estimates and invoices. To add this, go to Contacts > External Contacts and search for your Client’s Company name. Add the Tax Number under their address in the “Override Display Address” field.
If you’d like to add it above the address, you can also use the structured address fields and add the tax number to the “Address Line” field.
Click 'Save'. When you next create an invoice for this customer, the Client's Tax Number will be displayed under their address.