Let’s confirm first that your card is a 1k classic… can post the memory contents from a full scan? or confirm the ID is 4 bytes in the format XX:XX:XX:XX and not 7 bytes XX:XX:XX:XX:XX:XX:XX … that’s the first thing.
this is not a typical “old school” classic 1k … it’s a “new” “classic” “evolution 1” chip hah… so strange how they’ve painted themselves into a corner there.
In order to do anything with this chip, you will need a proxmark3 if there are any memory blocks that are protected with access bits. If they are all wide open with no access bits set and no data written, then you can get away with just cloning the ID into a flexM1 gen2 (but only the gen2) using an app called MCT and your phone… but if there are any access bits set, or if you want to use the xM1 or flexM1 gen1a, then you’re back to needing a proxmark3 to do the cloning.