Tax on private pensions after receiving state pension

Hi, I received my state pension in May 2024. I am in receipt of 2 private pensions. My understanding is tax will be deducted from my private pensions as I now exceed the current tax allowance. I informed HRMC online, the information given was confirmed as 'processed'. It is now 6 months and no tax has been deducted. Will I get a PAYE bill at the end of the tax year? I am a little confused regarding how the tax will be deducted. Thank you.

Hi
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