Still want to use "ptm" in XeLaTeX

There's nothing more than a visual comparison, showing that ptm is exactly the same as what you get with TeX Gyre Termes.

\documentclass{article}
\usepackage{amsmath}

\usepackage{fontspec}

\setmainfont{TeX Gyre Termes}
\newfontfamily{\OTIMES}{Times New Roman}

\def\fn"#1/#2"{#1}%

\begin{document}

{\OTIMES abcdefghijklmnopqrstuvwxyzfifl \expandafter\fn\fontname\font}

abcdefghijklmnopqrstuvwxyzfifl \expandafter\fn\fontname\font

{\fontencoding{OT1}\fontfamily{ptm}\selectfont
abcdefghijklmnopqrstuvwxyzfifl \fontname\font}

{\OTIMES ABCDEFGHIJKLMNOPQRSTUVWXYZ \expandafter\fn\fontname\font}

ABCDEFGHIJKLMNOPQRSTUVWXYZ \expandafter\fn\fontname\font

{\fontencoding{OT1}\fontfamily{ptm}\selectfont
ABCDEFGHIJKLMNOPQRSTUVWXYZ \fontname\font}

\itshape

{\OTIMES abcdefghijklmnopqrstuvwxyzfifl \expandafter\fn\fontname\font}

abcdefghijklmnopqrstuvwxyzfifl \expandafter\fn\fontname\font

{\fontencoding{OT1}\fontfamily{ptm}\selectfont
abcdefghijklmnopqrstuvwxyzfifl \fontname\font}

{\OTIMES ABCDEFGHIJKLMNOPQRSTUVWXYZ \expandafter\fn\fontname\font}

ABCDEFGHIJKLMNOPQRSTUVWXYZ \expandafter\fn\fontname\font

{\fontencoding{OT1}\fontfamily{ptm}\selectfont
ABCDEFGHIJKLMNOPQRSTUVWXYZ \fontname\font}

\end{document}

As you can also see, also the italic font in TeX Gyre Termes matches ptm, although there are small differences in kerning.

Define an own fontface. If you are using one of the KOMA-Script classes you can define the headers in an easy way to use Times.

\documentclass{article}
\usepackage{amsmath}
\usepackage{unicode-math}
%\setmainfont{what ever you want}
\newfontface\Times{Times New Roman MT Std}% I have only this otf version
\begin{document}
Latin Modern

{\Times $a=0 \text{ if needed}$}

\section{LatinModern}
\subsection{\Times Times New Roman} 
foo \Times foo
\end{document}