Notation parse rule does parse when it acts as a argument

It's not very clear what problem you are trying to solve here. Normally, you would use such a call to the Notation package to introduce a pretty way of displaying some Mathematica object. Here that is unnecessary as Mathematica does what you are asking automatically.

I infer that you are wanting a simplified notation for entering a TransferFunctionModel. One way to do this is with

totf[expr_] := TransferFunctionModel[{{expr}}, First[Cases[expr, _Symbol, ∞]]]

This lets you do

In my opinion, the Notation package is probably best left to advanced users of Mathematica. I would advise you to learn the basics first. However, you can use the function totf to define a notation.