Hi aah2024,
As your private work is not taxed at source via PAYE, you will need to register for Self employment (as a Sole Trader) to declare this income.
Once you have registered, you can declare this income in your usual Self Assessment return, by completing the Self Employment pages (while still declaring your regualr PAYE income in the Employment pages).
To register as a Sole Trader, go here:
What a sole trader is
Further guidance can be found here on how to complete your Self Assessment tax return.
HMRCgovuk
Or for more advice, contact us by webchat or phone here:
Self Assessment: general enquiries
Thank you.