In LaTeX, does it exist any symbol for

There is no ready made symbol per se, but you can definitely create a new one.
Simply define a new macro using either \mathbin or \mathrel. I think that you will need the later one, since an arrow usually shows a relation.
Please see here two understand the subtle differences between the two solutions.
You use the \overset command to stack up your operators.
Anyway here is your solution.
\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\newcommand{\leftrightarrowtriangleqbin}{\mathbin{\overset\triangleq\leftrightarrow}}
\newcommand{\leftrightarrowtriangleqrel}{\mathrel{\overset\triangleq\leftrightarrow}}
\begin{document}
$S \leftrightarrowtriangleqbin T$
$S \leftrightarrowtriangleqrel T$
\end{document}
And here is a sample output.

See the subtle spacing difference between the two?
Actually, for the second one \mathrel around the construction is redundant.
As pointed out by egreg below, \overset will keep the binary relation nature of its second argument.
Here are two possible alternatives. In both cases (\symA and \symB), I use both a left and right arrow joined in order to get a wider arrow. The \mkern can be increased negatively, if you want the width narrower. The \symA uses the \triangleq component from amssymb, but the vertical gap can be controlled with the optional argument to \stackon. The \symB does not require amssymb, but tries to mimic the tapered equal sign you showed in your figure, by using stacked \rules. Again, the vertical spacings are adjustable.
\documentclass{article}
\usepackage[usestackEOL]{stackengine}
\usepackage{amssymb}
\def\symA{\mathrel{\stackon[-0.8pt]{\leftarrow\mkern-6mu\rightarrow}%
{\scriptstyle\triangleq}}}
\def\symB{\mathrel{\stackon[.7pt]{\leftarrow\mkern-6mu\rightarrow}%
{\setstackgap{S}{0pt}\Shortstack{%
\scriptscriptstyle\triangle\\\rule[.8pt]{6pt}{0.25pt}\\\rule{8pt}{.25pt}}}}}
\stackMath
\begin{document}
$A \symA B \symB C$
\end{document}

\DeclareMathOperator? Just a new command with\mathrelenclosing the code… – Manuel Dec 29 '13 at 16:30\DeclareMathOperatorwhich is not suited for this situation. By the way, an arrow usually shows a relation. Like (almost?) all the arrows defined in Latex, I would use\newcommand\leftrightarrowtriangleq{\mathrel{\overset\triangleq\leftrightarrow}}. – Manuel Dec 29 '13 at 16:41\overset{\triangleeq}{\leftrightarrow}is sufficient, because\oversetwill keep the "binary relation" nature of its second argument. So\mathrelaround the construction is redundant. – egreg Dec 29 '13 at 16:53