\documentclass[a4paper]{article}
\usepackage{libertinus-otf}
\usepackage[fallback]{xeCJK}
\begin{filecontents}{morenameparts-cjk.dbx}
\ProvidesFile{cjk-names.dbx}[2016/07/24 extended name format for biblatex]
\DeclareDatamodelConstant[type=list]{nameparts}{prefix,family,suffix,given,cjk}
\end{filecontents}
\usepackage[
backend=biber,
style=authoryear,
datamodel=morenameparts-cjk,
]{biblatex}
\DeclareSortingNamekeyTemplate[cjk]{
\keypart{
\namepart{family}
}
\keypart{
\namepart{given}
}
\keypart{
\namepart{cjk}
}
}
\DeclareUniquenameTemplate[cjk]{
\namepart[base=true]{family}
\namepart[disambiguation=full]{given}
\namepart[disambiguation=full]{cjk}
}
\newbibmacro*{name:cjk}[3]{%
\usebibmacro{name:delim}{#2#3#1}%
\usebibmacro{name:hook}{#2#3#1}%
\mkbibnamefamily{#1}%
\ifdefvoid{#2}{}{\bibnamedelimd\mkbibnamegiven{#2}}%
\ifdefvoid{#3}{}{\bibnamedelimd\mkbibnamecjk{#3}}}
\newbibmacro{labelname:western}{%
\ifcase\value{uniquename}%
\usebibmacro{name:family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}%
\or
\ifuseprefix
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffixi}}
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefixi}
{\namepartsuffixi}}%
\or
\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}%
\fi
\usebibmacro{name:andothers}}
\newbibmacro{labelname:cjk}{%
\iffieldequalstr{uniquepart}{base}%
{\usebibmacro{name:cjk}
{\namepartfamily}
{\empty}
{\empty}}
{\iffieldequalstr{uniquepart}{given}%
{\usebibmacro{name:cjk}
{\namepartfamily}
{\namepartgiven}
{\empty}}
{\usebibmacro{name:cjk}
{\namepartfamily}
{\namepartgiven}
{\namepartcjk}}}}
\DeclareNameFormat{labelname}{%
\ifuniquenametemplatename{cjk}
{\usebibmacro{labelname:cjk}}
{\usebibmacro{labelname:western}}%
\usebibmacro{name:andothers}}
\DeclareNameFormat{family-given}{%
\ifsortingnamekeytemplatename{cjk}
{\usebibmacro{name:cjk}{\namepartfamily}{\namepartgiven}{\namepartcjk}}
{\ifgiveninits
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}}%
\usebibmacro{name:andothers}}
\DeclareNameFormat{given-family}{%
\ifsortingnamekeytemplatename{cjk}
{\usebibmacro{name:cjk}{\namepartfamily}{\namepartgiven}{\namepartcjk}}
{\ifgiveninits
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}}%
\usebibmacro{name:andothers}}
\DeclareNameFormat{family-given/given-family}{%
\ifsortingnamekeytemplatename{cjk}
{\usebibmacro{name:cjk}{\namepartfamily}{\namepartgiven}{\namepartcjk}}
{\ifnumequal{\value{listcount}}{1}
{\ifgiveninits
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}
\ifboolexpe{%
test {\ifdefvoid\namepartgiven}
and
test {\ifdefvoid\namepartprefix}}
{}
{\usebibmacro{name:revsdelim}}}
{\ifgiveninits
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}}}
\usebibmacro{name:andothers}}
\begin{filecontents}{\jobname.bib}
@book{zhaos,
title = {A Nation-State by Construction},
subtitle = {Dynamics of Modern {Chinese} Nationalism},
author = {given=Suisheng, family=Zhao, cjk=趙歲升, nametemplates=cjk},
year = {2011},
address = {Stanford},
publisher = {Stanford University Press},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\autocite{zhaos}
\printbibliography
\end{document}
biblatexstyles. You just need to copy it and changechicago-authordate.dbxto<name of the style you want to use>.dbx(e.g.authoryear.dbx). – moewe Sep 01 '21 at 16:02