Let's say that Alice is the administrator of a group. For each message generated by a group member, Alice uses an administrator's private key ($sk$) to sign it, indicating that this message has been checked by her. One day, Bob takes over from Alice. Therefore, Alice sends Bob the $sk$ in a secure channel. But the security concern is that since $sk$ is not changed, Alice still has the ability to sign messages using the $sk$. So I wonder if there is any cryptography technology that can prevent Alice from using this $sk$ after it is sent to Bob.
More generally, this question can be described as follows: Is there a way to transfer the ability to sign from A to B while keeping the same public key and preventing A from signing after the transfer is complete? (If needed, it is okay to change $sk$ as long as other requirements are satisfied.)