It's an example of the amsmath bug with nested accents dealt with in Why do arguments to nested \tilde or \breve commands reappear when amsmath is used?Why do arguments to nested \tilde or \breve commands reappear when amsmath is used? and that manifests itself when the inner accent is placed over multiple symbols.
My suggestion is to define an \Opring operator, rather than using \mathring\Op, with low level trickery that doesn't use math accents.
\documentclass{article} \usepackage{mathtools} \DeclareMathOperator{\Op}{Op} \DeclareMathOperator{\Opring}{% \text{\vbox{\offinterlineskip \halign{##\cr \hidewidth\r{}\hidewidth\cr \noalign{\kern-1ex} $\Op$\cr }% }}% } \begin{document} \[ 1 + \mathring\Op(4) = 2 \] % just for comparison \[ \overline{ 1 + \Opring(4) } = 2 \] \[ \mathring{\overline{ 1 + \Opring(4) }} = 2 \] \end{document} 