\documentclass{article}

\newenvironment{fooenv}
  {\bfseries}
  {}

\newenvironment{barenv}
  {\itshape}
  {}

\begin{document}

\begin{fooenv}
  Here is some foo.
\end{fooenv}

\begin{barenv}
  Here is some bar.
\end{barenv}

\let\oldfooenv\fooenv
\let\endoldfooenv\endfooenv

\renewenvironment{fooenv}
  {\begin{barenv}
    \begin{oldfooenv}}
  { \end{oldfooenv}
   \end{barenv}}

\begin{fooenv}
  Here is some foo.
\end{fooenv}

\end{document}