As Aditya already pointed out, using a doublesided layout is necessary. Otherwise there is no concept of a right page. By default the first page, the table of contents (when
\completecontent is used) and the parts already start on a right page.
However, the placement is customizable. All structure head commands have a
page key that either take
yes or a page break definition as an argument. For more details see the ConTeXt wiki - Titles. Using a
\definepagebreak definition is more powerful, since you can set the page headers as well.
And you can always use the
\page command in your document. To separate content and layout I would advice to avoid the use of direct instructions like
\page if possible.
% switch from singlesided to doublesided layout
% you have lots of options to influence the appearence of the page
% \definepagebreak [chapterpagebreak] [yes, header, right]
\definepagebreak [chapterpagebreak] [right]
% either use a page break definition
\setuphead [chapter] [page=chapterpagebreak]
% or a direct instruction without page break definition
% \setuphead [chapter] [page=right]
\setuphead [part] [page=right, placehead=yes]
\startstandardmakeup [align=middle, style=\bfd]
\startpart [title=Part one]