Declaring State Pension?

I have just received my first payment of State Pension from the DWP and I live abroad, will then inform you automatically under my PAYE, and adjust my tax code accordingly?

Hi Ian,
The DWP will notify HMRC automatically within 7 days of your state pension starting so your tax records can be updated. If you have a PAYE source of income in the UK, your tax code will be amended and a new tax code issued. You can ensure your tax records are correct by logging into the personal tax account.Personal tax account: sign in or set up.
Thank you.