As noted in https://tex.stackexchange.com/a/574078, you do not necessarily need decorations to add an arrow. A sloped pic also works. You can put it on the segment you want, which can be an advantage or disadvantage depending on the scenario.
\documentclass[11pt]{amsart}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,knots}
\begin{document}
\begin{tikzpicture}[pics/arrow/.style={code={%
\draw[line width=0pt,{Computer Modern Rightarrow[line
width=0.8pt,width=1.5ex,length=1ex]}-] (-0.5ex,0) -- (0.5ex,0);
}}]
\begin{knot}[clip width=10, clip radius=15pt, consider self intersections,
end tolerance=3pt]
\strand[thick] (0,0)
to[out=up, in=down] (0,0.7)
to[out=up, in=left] (0.5,1.5)
to[out=right, in=up] pic[pos=0.5,sloped]{arrow}(1,1)
to[out=down, in=right] (0.5,0.5)
to[out=left, in=down] (0,1.3)
to[out=up, in=down] (0,2);
\end{knot}
\end{tikzpicture}
\end{document}

It is easy to change any aspect of the arrow. Apart from the obvious possibility of editing the pic you can just add an optional argument.
\documentclass[11pt]{amsart}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,knots}
\begin{document}
\begin{tikzpicture}[pics/arrow/.style={code={%
\draw[line width=0pt,{Computer Modern Rightarrow[line
width=0.8pt,width=1.5ex,length=1ex,#1]}-] (-0.5ex,0) -- (0.5ex,0);
}}]
\begin{knot}[clip width=10, clip radius=15pt, consider self intersections,
end tolerance=3pt]
\strand[thick] (0,0)
to[out=up, in=down] (0,0.7)
to[out=up, in=left] (0.5,1.5)
to[out=right, in=up] pic[pos=0,sloped]{arrow={scale=2,line
width=1.6pt}}(1,1)
to[out=down, in=right] (0.5,0.5)
to[out=left, in=down] (0,1.3)
to[out=up, in=down] (0,2);
\end{knot}
\end{tikzpicture}
\end{document}

Note also that sometimes one needs the allow upside down key as in https://tex.stackexchange.com/a/574078.
allow upside downkey? – nog642 Sep 19 '23 at 06:05