When an Enrollment Agent creates a new smart card certificate, a new key pair is created and assigned to that user in Active Directory. Note that the Enrollment Agent's key is not written anywhere - the HSM helps create a brand new (cryptographically random) key pair. The new pair is sent out from the HSM and written to the smart card.
If the user being enrolled by the Enrollment Agent already has a key, it just gets a new one that will work equally well in certificate-based authentication. The HSM doesn't have to know any existing private keys to create a new one.
Further reading: Certificate enrollment using smart cards, Enroll for Certificates on Behalf of Other Users, Using the nCipher Hardware Security Module