This is not as trivial as it may seem to be.
The 2nd PS UART can only be connected into the PL, as there aren’t any physical connectors available on either of those boards to connect it to, so yes, you would need to modify the PL design.
As it is a PS UART, you would need to modify the Linux device tree. Then you would need to write C/Python to control this UART.
What are you trying to do? If you need to control a “UART” peripheral, the Arduino IOP subsystem (MicroBlaze based system) in the base overlay for the PYNQ-Z1 has a UART already connected. You could write some C code for the MicroBlaze to control a UART peripheral.
You could also add a new MicroBlaze to control the UART, and again write some C code to manage the UART interface.
This would probably be the way I would approach this. Depending on what you need to do/your experience and prior knowledge, you may prefer to do this a different way.
Cathal