Simultaneous overset and superscript

My impression is that you're using the wrong tool:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

$\mathring{Z}^\lambda$

\end{document}

If you really want a bigger circle, then something like

\newcommand{\rZ}{%
  \vphantom{\rrZ}% get the height right
  \smash{\rrZ}% print the item without height
  {\vphantom{Z}}% provide a atom the superscript is attached to
}
\newcommand{\rrZ}{\overset{\scriptscriptstyle\,\circ}{Z}}

can do.

The accents package lets you define circ as a math accent. The result is slightly larger than \mathring. Note in the \overset solution, \circ is not well placed (horizontally speaking):

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}

\usepackage{accents}

\begin{document}

\begin{tabular}{ccc}
  \verb+\overset+ & \verb+\mathring+ & \verb+\accentset+ \\[2ex]
  $ \smash[t]{\overset{\circ}{Z}}^\lambda $ & $ \mathring{Z}^\lambda $ & $ \accentset{\circ}{Z}^\lambda $
\end{tabular}

\end{document} 

Slight variation that saves typing

\documentclass{article}
\usepackage{amsmath}
\newcommand\cZ{\overset{\circ}{Z}\vphantom{Z}}
\begin{document}
$\cZ^\lambda$
\end{document}