If a director goes abroad and pays for hotel, taxi, meal etc. (all related to the business and will be reimbursed by the company's client) and is charged that country VAT, shall it be treated as an out of scope of VAT ?
What is the procedure within the EU states and outside?
You can recover VAT incurred in other Member States. Notice 723A, chapter 2 gives details of this.
Strictly, therefore, the net amount is recoverable from the company's client. Remember to add UK VAT (if applicable) to the amount, as it is part of the value of the supply to the client.
Where VAT is incurred outside the EU, recovery is not so easy, and depends on the specific rules applying to that country.