If I understand your question correctly, you want to move the axis. TikZ of course trims the picture. But if you put \path (coordinate); with some suitable coordinate there will be space to the left, to the right, above and/or below the axes, depending on your choice of (coordinate). Here are two examples, which are, by relativity, equivalent.
\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\begin{tikzpicture}
% The axes
\path(0,0);
\begin{scope}[xshift=3cm]
\draw[->] (xyz cs:x=-1.5) -- (xyz cs:x=1.5) node[above] {$x$};
\draw[->] (xyz cs:y=-1.5) -- (xyz cs:y=1.5) node[right] {$z$};
\draw[->] (xyz cs:z=-1.5) -- (xyz cs:z=1.5) node[above] {$y$};
\end{scope}
\end{tikzpicture}
\begin{tikzpicture}
% The axes
\path(-3,0);
\draw[->] (xyz cs:x=-1.5) -- (xyz cs:x=1.5) node[above] {$x$};
\draw[->] (xyz cs:y=-1.5) -- (xyz cs:y=1.5) node[right] {$z$};
\draw[->] (xyz cs:z=-1.5) -- (xyz cs:z=1.5) node[above] {$y$};
\end{tikzpicture}
\end{document}

\documentclassand ended with\end{document}. What happened to that ability? And you'd greatly benefit from explaining what "centre of the screen" means. – Jun 09 '18 at 02:52