System Photo Library on old Mac but not the new one

Hello,

I used migration assistant to transfer data from old mac to new one but the System Photo Library is still on the old mac and therefore I cannot share photos or directly upload from the new Mac's library. I am keeping the old Mac as a personal computer and the other one id for work. Can't i have a system photo library on each computer ? If yes, how do I make the new Mac's library, the system photo library? Thanks !