Can you derive ed25519 keys from secp256k1? Alice has a secp256k1 key pair that she used some time ago when she communicated with Bob. Bob can no longer user secp256k1 but he only uses ed25519 instead.

Is there a secure algorithm that Bob can use to derive an ed25519 pubkey from original Alice's secp256k1 pub key and also Alice can derive the matching ed25519 private key from her original secp256k1 private key such that they can communicate securely via ed25519 encrypted messages?

Thanks!
No. They use different curves. 

For each system the public and private keys of the same key pair are not independent. You choose a private key and that determines what your public key will be. 

(Good thing it doesn't work in reverse. If you could derive someone's private key from their public key, then we wouldn't have an asymmetric algorithm.)

You can derive a private key from an old public key. (Wrong!) Or a private key from an old private key. But you cannot derive a public key directly from anything other than its corresponding private key.

Alternatively Alice can sign, using her old private key, a messages that informs others of her new public keys. When Bob wants to communicate with her, he can check the authenticity of that message using Alice's old public key. (Assuming the old private key has not been compromised.)

(Note that you should be using separate keys for signing and encrypting.)

As for Alice's private key, I recommend generating new (random) private keys. If her old private key were compromised then it would mean all new deterministically derived private keys would automatically be compromised as well.