Update 1: after the correct comment of @Vincent
After many attemps and looked the manual of MnSymbol
I have taken all the fonts of type MnSymbolC


etc...and with \DeclareMathSymbol{\thinstar
}{\mathbin}{MnSyC}{134
} I have obtained only the \thinstar
operator (code 134).
\documentclass[a4paper,12pt]{article}
\usepackage{newtxtext}
\usepackage{newtxmath}
\DeclareFontFamily{U} {MnSymbolC}{}
\DeclareFontShape{U}{MnSymbolC}{m}{n}{
<-6> MnSymbolC5
<6-7> MnSymbolC6
<7-8> MnSymbolC7
<8-9> MnSymbolC8
<9-10> MnSymbolC9
<10-12> MnSymbolC10
<12-> MnSymbolC12}{}
\DeclareFontShape{U}{MnSymbolC}{b}{n}{
<-6> MnSymbolC-Bold5
<6-7> MnSymbolC-Bold6
<7-8> MnSymbolC-Bold7
<8-9> MnSymbolC-Bold8
<9-10> MnSymbolC-Bold9
<10-12> MnSymbolC-Bold10
<12-> MnSymbolC-Bold12}{}
\DeclareSymbolFont{MnSyC} {U} {MnSymbolC}{m}{n}
\SetSymbolFont{MnSyC} {bold}{U} {MnSymbolC}{b}{n}
\DeclareMathSymbol{\thinstar}{\mathbin}{MnSyC}{134}
\begin{document}
$\sum_{i=1}^n g\thinstar f \cup R$
or other
\[\sum \sigma_s\prod a_i\]
\end{document}
It seem that the symbols are all of newtxmath

if we compare with \sum
and \prod
of MnSymbol (for example),

I add some proposals....
\documentclass[11pt]{article}
\usepackage{newtxtext}
\usepackage{newtxmath}
\usepackage{MnSymbol}
\usepackage{wasysym}
\begin{document}
\( f \star g \), \verb|classic star|
\( f \mathbin{\filledstar} g \), \verb|MnSymbol package|
$f \mathrel{\thinstar} g $, \verb|MnSymbol package|
$f \mathbin{\APLstar} g $, \verb|Table 330: wasysym APL Symbols|
\end{document}
