As far as I can tell, you're abusing and misusing the threeparttable
machinery. For one, you're not actually including the \caption
directive -- one of the three formal parts of a threepartable
-- in the threeparttable
environment. Second, if your objective is to typeset a table that's considerably wider than the text block, you should go about this quite differently from what you show in your posting. Third, the primary purpose of the tablenotes
environment is to typeset footnote text associated with \tnote
directives; however, your code doesn't include any \tnote
s.
I also don't understand why you employ fixed-width p
-type columns instead of X
-type columns (provided by the tabularx
package).
The following screenshot shows two separate solutions that employ tabularx
environments. The first uses a threeparttable
environment (with \begin{tablenotes}[flushleft]
); the second does not -- and thereby demonstrates that it's not necessary to deploy the threeparttable
machinery in order to achieve your formatting objective.

\documentclass{article}
\usepackage{threeparttable,bigstrut}
\usepackage{tabularx}
\begin{document}
\begin{table}[htbp]
\begin{threeparttable}
\caption{Solution with \texttt{threeparttable}}
\label{tab:1}
\begin{tabularx}{\textwidth}{@{} *{9}{X} @{}}
\hline
\multicolumn{3}{@{}l}{$h=1$} &
\multicolumn{3}{l}{$h=12$} &
\multicolumn{3}{l}{$h=60$}\bigstrut\\
\hline
Ind & $\hat{\lambda}$ & $R^2$ &
Ind & $\hat{\lambda}$ & $R^2$ &
Ind & $\hat{\lambda}$ & $R^2$\bigstrut\\
\hline
Ag & \textbf{9.82*} & 0.43 & Ag & 1.79 & 0.09 & Agric & -0.23 & 0.03\bigstrut\\
Frr & 3.09 & 0.1 & Frr & -0.67 & 0.03 & Frr & -0.29 & 0.05 \\
Brr & 5.97 & 0.26 & Brr & 2.23 & 0.2 & Brr & 0.39 & 0.06 \\
\hline
\end{tabularx}
\begin{tablenotes}[flushleft]
\item[]Notes: In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper.
\end{tablenotes}
\end{threeparttable}
\end{table}
\begin{table}[htbp]
\caption{Solution without \texttt{threeparttable}}\label{tab:2}
\smallskip
\begin{tabularx}{\textwidth}{@{} *{9}{X} @{}}
\hline
\multicolumn{3}{@{}l}{$h=1$} &
\multicolumn{3}{l}{$h=12$} &
\multicolumn{3}{l}{$h=60$}\bigstrut\\
\hline
Ind & $\hat{\lambda}$ & $R^2$ &
Ind & $\hat{\lambda}$ & $R^2$ &
Ind & $\hat{\lambda}$ & $R^2$\bigstrut\\
\hline
Ag & \textbf{9.82*} & 0.43 & Ag & 1.79 & 0.09 & Agric & -0.23 & 0.03\bigstrut\\
Frr & 3.09 & 0.1 & Frr & -0.67 & 0.03 & Frr & -0.29 & 0.05 \\
Brr & 5.97 & 0.26 & Brr & 2.23 & 0.2 & Brr & 0.39 & 0.06 \\
\hline
\end{tabularx}
\smallskip
Notes: In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper In this paper in this paper in this paper.
\end{table}
\end{document}
\begin{tablenotes}[flushleft] \setlength\labelsep{0pt} \item[]Note:...
should work. (See also: tex.stackexchange.com/a/539880/134144)\hspace*{-1in}
right before\begin{tabular}
?