This has nothing to do with parentheses following the superscripted symbol:
\documentclass{article}
\usepackage{amsmath}
\let\originalleft\left
\let\originalright\right
\renewcommand{\left}{\mathopen{}\mathclose\bgroup\originalleft}
\renewcommand{\right}{\aftergroup\egroup\originalright}
\begin{document}
$P^{N}\!\originalleft(K\originalright)$
$P^{N}\left(K\right)$
$P^{N}(K)$
$P^{N}K$
\end{document}

The \! in the first case is for removing the thin space normally inserted by \left. As you can clearly see, the spacing is exactly the same in all four cases. It depends on the \scriptspace feature: after a subscripted or superscripted symbol, TeX adds horizontal space in the amount of \scriptspace, default 0.5pt.
If you also consider that math letters are slanted and the left parenthesis has a “hole” in the left upper corner, the space appears to be bigger than it really is. But there are very good reasons for this.
You can have a fairer comparison by using upright characters and, for the superscript, something that has no sidebearings:
\documentclass{article}
\newcommand{\thinbar}{{\vphantom{|}\vrule width .2pt}}
\begin{document}
$\mathrm{I}^{\thinbar}\thinbar\mathrm{I}$ $\mathrm{I}^{\mathrm{I}}\mathrm{I}$
\setlength{\scriptspace}{0pt}
$\mathrm{I}^{\thinbar}\thinbar\mathrm{I}$ $\mathrm{I}^{\mathrm{I}}\mathrm{I}$
\end{document}

In the left column you clearly see the effect of \scriptspace; in the right column you can compare the effect with “real” superscripts. The purpose of \scriptspace is exactly that of slightly detaching symbols for better reading.
Important note
I left your redefinition of \left and \right, but I can't recommend it in any way. There's already a package doing it much better, mleftright.
\documentclass{...}, the required\usepackage's,\begin{document}, and\end{document}. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to give you a hand. Help them help you: remove that one hurdle between you and a solution to your problem. – Adam Liter Jul 23 '14 at 06:02\left(and\right)unless it's really necessary. In this case, it's not, so just use\mathscr{P}^N(\mathscr{K}). – Werner Jul 23 '14 at 06:04$P^N\left(K\right)$ $P^N\bigl(K\bigr)$ $P^N(K)$– Werner Jul 23 '14 at 06:23(. You can bring them closer using\!(yielding the fourth entry in the image link). – Werner Jul 23 '14 at 06:30mleftrightpackage; however, I'd simply prefer using\leftand\rightonly when really necessary. For example, in$\mathscr{P}^{N}\left(\mathscr{K}\right)$they are unnecessary. – egreg Jul 23 '14 at 08:48