\documentclass{article}

\usepackage[version=3]{acro}

\DeclareAcroEnding{possessive}{'s}{'s}

\NewAcroCommand\acg{m}{\acropossessive\UseAcroTemplate{first}{#1}}
\NewAcroCommand\acsg{m}{\acropossessive\UseAcroTemplate{short}{#1}}
\NewAcroCommand\aclg{m}{\acropossessive\UseAcroTemplate{long}{#1}}
\NewAcroCommand\acfg{m}{%
  \acrofull
  \acropossessive
  \UseAcroTemplate{first}{#1}%
}
\NewAcroCommand\iacsg{m}{%
  \acroindefinite
  \acropossessive
  \UseAcroTemplate{short}{#1}%
}

\DeclareAcronym{MP}{
  short            = MP ,
  long             = Member of Parliament ,
  long-plural-form = Members of Parliament ,
  long-possessive-form = Member's of Parliament
}

\begin{document}

\acg{MP} \par
\acsg{MP} \par
\aclg{MP} \par
\acfg{MP} \par
\iacsg{MP} \par

\end{document}
