UART 1-way communication

I'm making a project, and it's limited to only 1 wire to connect 2 Arduinos to carry a 4-bit sequence in 1-way only.
Can I use UART as 1-way communication to transmit data from Arduino 1 to Arduino 2 only?
Or It's necessary to connect both Tx and Rx even if I only need 1-way communication?

Also another question, idk if its a stupid one or not but does Arduino nano have UART ports?

Yes.

It has one hardware UART port, used for uploading programs.

Yes, transmit and receive are separate parts of the Universal Asynchronous Receiver-Transmitter port.
Consider that RX and TX can connect to different chips even! Yeah, read from one chip and transmit to another, that can be chained.

When you code serial, reads and writes can be handled independently.

and for serial data transfers like communication with Serial Monitor.

Thank you

After uploading the code can I keeping it running on an external power source? and use the UART port to communicate with the the other Arduino?

Yeah, true I forgot to mention that it's 2 wires because the second was for common ground.

He will need a ground wire to the chassis.
I once had VW Type-3's. All of those old VW's ran a 'hot' chassis! There was a reason but it eludes me now!

That's nice to know.

Thank you so much!

Once you load the hex file (what the compiler makes from your source code), you can turn it off and on and use serial for communication which is the primary reason that the port is there. Programs can be loaded through the ICSP port which is how bootloaders get loaded to make loading through serial possible, but not required just easier.