Hi,
Please have a look at article 17 of the UK / Austria tax treaty at the link below for your private pension.
UK/Austria Double Taxation Agreement
Your state pension will be taxable in Austria. To ensure that no tax is deducted from your UK pensions, once you have commenced receipt of them, please complete the DT individual form and send the signed form to the Austrian tax authorities. They will validate the forma and return it to you.
You then send the validated form to HMRC BX9 1AS (the address in on the form).
Thank you.