Use the shared third-party repo as a submodule under the app repo

When updated:

git submodule init;git submodule update;

I don’t know what language and platform you are using. Generally, popular platforms will provide something called a package manager.
The package manager is used to solve the reference management of class libraries between projects to meet your needs.
The official will generally provide a public source and provide some classic and popular packages.
Here are the package managers for several platforms that I know about:
.net:nuget
ruby:gem
nodejs:npm