How do I change my Bitcoin wallet address?

Could you please elaborate on the steps involved in changing a Bitcoin wallet address? I'm particularly interested in understanding if this process requires the creation of a new wallet entirely, or if there's a way to simply update the existing one. Additionally, I'd like to know if there are any security considerations or potential risks involved in making such a change, especially if my wallet holds significant amounts of Bitcoin. I'm also curious about whether this process differs depending on the type of wallet I'm using, such as a hardware wallet or a mobile wallet.