I would use the in and out keys (and make the matrix a bit bigger so that the annotations do not clash with the matrix entries).
\documentclass{article}
\usepackage{tikz}
\usepackage{nicematrix}
\begin{document}
$\begin{vNiceMatrix}[first-row,columns-width=1.5em]
u & v \\
x & x' \\
y & y'
\CodeAfter
\begin{tikzpicture}
\path (1-1.east) -- node[below=0.35em,red,inner sep=0pt] (minus) {$-$} (1-2.west);
\draw [red,->]
(1-1.east) to[out=0,in=30] (minus.south east)
to[out=-150,in=-30] (minus.south west)
to[out=150,in=180] (1-2.west);
\end{tikzpicture}
\end{vNiceMatrix}$
\end{document}

Or maybe also make sure that the arrow attaches at the same vertical position.
\documentclass{article}
\usepackage{tikz}
\usepackage{nicematrix}
\begin{document}
$\begin{vNiceMatrix}[first-row,columns-width=1.5em]
u & v \\
x & x' \\
y & y'
\CodeAfter
\begin{tikzpicture}
\path (1-1.east) -- node[below=0.35em,red,inner sep=0pt] (minus) {$-$} (1-2.west);
\draw [red,->]
(1-1.east) to[out=0,in=30] (minus.south east)
to[out=-150,in=-30] (minus.south west)
to[out=150,in=180] (1-1.east-|1-2.west);
\end{tikzpicture}
\end{vNiceMatrix}$
\end{document}

Or even more symmetric.
\documentclass{article}
\usepackage{tikz}
\usepackage{nicematrix}
\usetikzlibrary{calc}
\begin{document}
$\begin{vNiceMatrix}[first-row,columns-width=1.5em]
u & v \\
x & x' \\
y & y'
\CodeAfter
\begin{tikzpicture}
\path (1-1.east) -- node[below=0.35em,red,circle,inner sep=1pt] (minus) {$-$} (1-2.west);
\draw [red,->] let \p1=($(minus.east)-(minus.center)$) in
(1-1.east) to[out=0,in=150] (minus.60)
arc[start angle=60,end angle=-240,radius=\x1]
to[out=30,in=180] (1-1.east-|1-2.west);
\end{tikzpicture}
\end{vNiceMatrix}$
\end{document}

(1-1.east-|1-2.west)do the trick for the vertical position ? – projetmbc Jun 09 '20 at 20:41(1-1.east-|1-2.west)means "take the y component of1-1.eastand the x component of1-2.west). It is very nicely described in https://tex.stackexchange.com/a/401429 – Jun 09 '20 at 20:45($(1-1.east) + (0.05,0)$)(which can be translated to([yshift=0.5mm]1-1.east))? (Or are you looking for...([yshift=-0.5mm]1-1.east) coordinate (aux) ... (aux-|1-2.west)?) – Jun 12 '20 at 19:41shorten >=1pt,shorten <=1pt, say. – Jun 12 '20 at 20:19