how to inform the employer of my British passport

Hello!
I recently have become a British citizen and have received my new passport. The first passport was not EU.
Do I have to provide the new passport details to my employer, please? Is there a time limit?
The HR department pretty much ignore my questions about it. I want to make sure I am not breaking the law by them not having my new passport details.

Not required to update them. Presumably you did update the employer of your ILR.

Thank you very much! Yes, i did.