\documentclass[beamer]{standalone}
\usepackage{tikz}
\usetikzlibrary{external}
\tikzexternalize % activate! 
\begin{document}
\begin{standaloneframe}

% If overlays do not work, use \only<1-n>{...} where n is the max overlay
 \only<1-3>{
  \begin{tikzpicture}[]
    \coordinate(h0) at (0,0);
    \coordinate(h1) at (0,5);
    \coordinate(h2) at (0,10);
    \coordinate(h3) at (0,15);
%    \draw (h0) -- (h1);
    \draw[color=white] (h0) node {\Huge $\mathbb Q$} ;
    \draw<3-> (h0) node {\Huge $\mathbb Q$} ;
    \draw[color=white] (h1) node {\Huge $(S,<_{\mathbb Q})$} ;
    \draw<2-> (h1) node {\Huge $(S,<_{\mathbb Q})$} ;
    \draw[color=white] (h2) node {\Huge $(T,<_{\mathbb Q})$} ;
    \draw (h2) node {\Huge $(T,<_{\mathbb Q})$} ;
    \draw (h3) node {\Huge $\mathbb Q$} ;

%    \draw[->, thick] (h0) -- (h1) -- (h2) -- (h3);
    \draw<3->[->, line width=0.1cm] (0,1) -- (0,4);
    \draw<2->[->, line width=0.1cm] (0,6) -- (0,9);
    \draw[->, line width=0.1cm] (0,11) -- (0,14);
    
  \end{tikzpicture}
 }
\end{standaloneframe}
\end{document}

%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End: