Is it possible to derive a public key from another public key without knowing a private key (Ed25519)?
Yes! You can use the ephemeral key derivation mechanism that is for example used in Monero (they call it stealth keys there).

Consider public key $A=aG$, with private key $a$. Then, a derived key can be generated, parametrised by the random scalar $r$:

$$A'=H_s(rA)G+A$$

and the party that knows $a$ can use the public parameter $R=rG$ to compute their ephemeral private key $a'=H_s(aR)+a$. You can for example store $R$ with your signature.



Note 1: We add $A$ resp. $a$ to the public resp. private key to ensure that the party that derives a key cannot compute the private key.

Note 2: This derivation is basically a Diffie-Hellman key exchange with a random ephemeral key $R$.

Note 3: $R$ can also be used to "check" whether the user has access to this specific key. He just needs to check whether $A'=H_s(aR)+A$ holds.