As long as you have access to your 24 word seed, you can always restore your private-/public- keys.
The black security card is used as a physical 2FA as an additional security layer to the nano/wallet.
This card is only used to send funds from this specific hardware device. Its not related to your seed in any way.
You can import the seed into any BIP39 compatible wallet (e.g. electrum, can be downloaded here: https://electrum.org/#download).
Just choose to restore from seed and check the 'BIP 39 seed' option.
If you are holding quite 'large' amounts, i would recommend to make sure your PC is free from malware before typing in the seed. Better safe than sorry.
Note: Next time please start a new thread instead of hijacking/resuscitating an old one.