gpg-card currently supports authenticating to PIV applets with 3DES and performing various useful operations on the card. Modern cards are supplied with AES management keys and there is no way to authenticate to these cards.
piv-tool in OpenSC supposedly can do this but I could not find any useful documentation to allow me to do so.
Yubikey documentation lists their supported algorithms: "9B: Triple-DES key (algorithm 03) for PIV management. YubiKeys with firmware 5.4 and up also support AES-128 (algorithm 08), AES-192 (algorithm 0A) and AES-256 (algorithm 0C) keys for PIV management."
The card I'm using is a Gemalto IDPrime PIV 2.1 and is supplied with an AES-128 card management key.
I'm not sure if it's possible, but a workaround that allows swapping the AES-128 key for a 3DES key using another tool, then allowing management with gpg-card, would be a good bridging solution.