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
card.
"Generating smart-card stubs on a clean computer?" [1] explains that you need
the public key plus a run of --card-status to generate the stubs.
Problem:
current gnupg does not have a function to re-calculate the "stub" and the
"public key" from a secret key on your card.
Remark:
A manual, but quite difficult, solution was proposed in [2].
[1] http://lists.gnupg.org/pipermail/gnupg-users/2010-September/039488.html
[2] http://lists.gnupg.org/pipermail/gnupg-users/2014-October/051051.html