Need the height of the descent

Something like this?? I set the baseline to the depth of the g descender and the top of the arrow to the height of the X, using the active font size.

\documentclass{article}
\usepackage{tikz}

\newcommand{\increasing}{%
\setbox0=\hbox{Xg}%
\begin{tikzpicture}[baseline=\dp0]
\draw[->] (0,0) -- (1ex,\dimexpr\ht0+\dp0\relax);
\end{tikzpicture}
}
\begin{document}
\Large fg\increasing
\normalsize fg\increasing
\tiny fg\increasing
\end{document}

You can measure the maximum descender:

\documentclass{article}
\usepackage{tikz}

\newcommand{\showbaseline}{%
  \settodepth{\alphabetdepth}{fgjpqy}
  \makebox[0pt][l]{\vrule width 5cm height -\alphabetdepth depth \dimexpr\alphabetdepth+0.1pt\relax}%
  \ignorespaces
}

\newlength{\alphabetdepth}
\newcommand{\increasing}{%
  \settodepth{\alphabetdepth}{fgjpqy}%
  \begin{tikzpicture}[baseline=\alphabetdepth]
  \draw[->] (0,0) -- (1ex,1em);
  \end{tikzpicture}%
}
\begin{document}

\showbaseline
f \increasing\quad {g \increasing} {\itshape f \increasing}

\bigskip

{\LARGE\showbaseline f \increasing\quad g \increasing}

\bigskip

{\tiny \showbaseline\itshape f \increasing}

\end{document}

The \showbaseline command is just for making clear where the maximum depth is located.