Adjective for not first but either second, third, fourth, etc
Solution 1:
It very much depends on context.
In many/most contexts, anything that's "not first" is just subsequent, or later.
In OP's context, the best word might be other. It's hard to say.
Solution 2:
Depending on context, you might consider subsequent.
His first book was good, but the subsequent ones were bad.
His first wife was old, but the subsequent ones were young.