New math operator (EDIT: newcommand!) with parentheses and subscript

You can define \newcommand{\Tr}[1]{\operatorname{Tr}\left(#1\right)}.

I don't think you are going to save yourself much time by creating a math operator that takes a parenthesis-delimited argument.

Moreover, if you use \left and \right to auto-size the delimiters, you will end up with a typographically incorrect amount of space between Tr and the opening parenthesis. To avoid this incorrect spacing, I suggest you load the mleftright package and use \mleft( and \mright) instead of \left( and \right).

\documentclass{article}
\usepackage{mathtools}  % for '\DeclareMathOperator' macro
\DeclareMathOperator{\Tr}{Tr}
\usepackage{mleftright} % for '\mleft' and '\mright' macros

\begin{document}
$-\Tr(A)$ vs. $-\Tr\mleft(A\mright)$ vs. $-\Tr\left(A\right)$
\end{document}