I can't test it right now, but according to section 2.2. of the glossaries manual (and assuming a document class whose \chapter and \section macros at least resemble those of the standard classes), loading
\usepackage[section,numberedsection=autolabel]{glossaries}
in the preamble and issuing \printglossaries immediately after \appendix in the document body should do what you want.
EDIT: Minimal working example (including some speculation about your appendix numbering scheme):
\documentclass{report}
\usepackage[section,numberedsection=autolabel]{glossaries}
\makeglossaries
\newglossaryentry{electrolyte}{name=electrolyte,%
description={solution able to conduct electric current}}
\begin{document}
\chapter{First}
Some text about \gls{electrolyte}.
\appendix
\chapter*{Appendix}
\markboth{\MakeUppercase{Appendix}}{\MakeUppercase{Appendix}}
\renewcommand*{\thesection}{A.\arabic{section}}
\printglossaries
\end{document}
