Currently I have this 4 bit CPU as shown in the schematic diagram below.

What I wish to achieve:
-Add one more output register to make the CPU output a total of 8 bits
-Show alphabet using the 8 bits output

My current trial:
-Cout of the first IC connected to Cin of the second IC
-Cascaded in synchronous fashion

What I unsure/don't understand:
- Should I connect the A~D pins of the second register to ALU?
- The LOAD-bar pin is connected to LO-bar of the ALU. Should I add one more LO-bar to the ALU and connect it to the LOAD-bar of the second register?

 

what do you want to do with the counters ?
the 161 , has two enable inputs, CEP and CET, both must be high for the counter to count.
why two you ask, its to allow fast propagation of the "terminal count"

have look at fig 1 here
https://www.ti.com/lit/gpn/SN74S10?keyMatch=74LS161&tisearch=Search-EN-everything

btw: you do realise, the 161 has an async clear, whilst the 163 has the syn clear,

 

what do you want to do with the counters ?
the 161 , has two enable inputs, CEP and CET, both must be high for the counter to count.
why two you ask, its to allow fast propagation of the "terminal count"

have look at fig 1 here
https://www.ti.com/lit/gpn/SN74S10?keyMatch=74LS161&tisearch=Search-EN-everything

btw: you do realise, the 161 has an async clear, whilst the 163 has the syn clear,

Umm, is that the link you intended to share?

 

what do you want to do with the counters ?
the 161 , has two enable inputs, CEP and CET, both must be high for the counter to count.
why two you ask, its to allow fast propagation of the "terminal count"

have look at fig 1 here
https://www.ti.com/lit/gpn/SN74S10?keyMatch=74LS161&tisearch=Search-EN-everything

btw: you do realise, the 161 has an async clear, whilst the 163 has the syn clear,

I want to cascade the two counters so that I can have 8 bits output out of the 4 bit CPU.
Also, I am not sure about what do you mean by
"why two you ask, its to allow fast propagation of the "terminal count" "
, can you elaborate more on that, please?Thank you.

 

So you want an 8 bit, loadable counter ?
in that case you need to connect the loads of all counter chips.

You also need to connect up the CET and CEP pins as per the data sheet I linked to .

Just as a reference.
when these counters were common, back in the 80's I seem to remember that most new people using them in circuits made a mistake or two.
they are ridiculously simple but complicated.

Also note that in your original diagram, only one of the 161 is being used as a counter, the rest are just registers. A 374 would be a cheaper option for a register. You could also dispose of the 153 multiplexer in this case, and use the tri state outputs of the 374.. just check the timing.