User story and problem:
As a Smart Card user, your private keys is stored on your smart card, and the
secret keyring on your main computer has only a so-called "stub" (pointer) to
your secret key in it. When you decided not to store the public key [sic]
elsewhere, for example, when you have forgotten to store that when you generated
your private key, you cannot recreate the public key from the secret key on your
"Generating smart-card stubs on a clean computer?"  explains that you need
the public key plus a run of --card-status to generate the stubs.
current gnupg does not have a function to re-calculate the "stub" and the
"public key" from a secret key on your card.
A manual, but quite difficult, solution was proposed in .