I'm not sure what you want to happen in the case of unnumbered chapters, so I've omitted that formatting here. I'm also not clear whether you want to move the line or eliminate it, so I show examples of both.
I've also commented the code concerning the setting of the page dimensions since your settings are not possible (i.e. memoir
cannot implement the numbers you request in your MWE as you discover if you ask it to check).
You can eliminate the line altogether:
\documentclass[a4paper,11pt,oneside,showtrims,openright,titlepage]{memoir}
\makechapterstyle{VZ23}{%
\renewcommand\chapternamenum{}%
\renewcommand\printchaptername{}%
\renewcommand\chapnumfont{\Huge\bfseries\centering}%
\renewcommand\chaptitlefont{\Huge\scshape\centering}%
}
\trimFrame
\settrims{3cm}{5.2cm}
\settrimmedsize{210mm}{140mm}{*}% the third argument is the ratio of the first to the second
\settypeblocksize{170mm}{95mm}{*}% ditto
\setlrmargins{*}{*}{1}% without this, things don't fit on the page!
\setulmargins{*}{*}{1}% ditto
\checkandfixthelayout% you need this after changing the page layout above!
\chapterstyle{VZ23}
\begin{document}
\chapter[NOTIZIA]{NOTIZIA}
\end{document}

Or you can put the line before the chapter number as in the image in your question:
\documentclass[a4paper,11pt,oneside,showtrims,openright,titlepage]{memoir}
\makechapterstyle{VZ23}{%
\renewcommand\chapternamenum{}%
\renewcommand\printchaptername{\par\nobreak\vskip\midchapskip\hrule\vskip\midchapskip}%
\renewcommand\chapnumfont{\Huge\bfseries\centering}%
\renewcommand\chaptitlefont{\Huge\scshape\centering}%
}
\trimFrame
\settrims{3cm}{5.2cm}
\settrimmedsize{210mm}{140mm}{*}% the third argument is the ratio of the first to the second
\settypeblocksize{170mm}{95mm}{*}% ditto
\setlrmargins{*}{*}{1}% without this, things don't fit on the page!
\setulmargins{*}{*}{1}% ditto
\checkandfixthelayout% you need this after changing the page layout above!
\chapterstyle{VZ23}
\begin{document}
\chapter[NOTIZIA]{NOTIZIA}
\end{document}
