Timelink, formerly known as MHK (Micro History with Kleio) is an information system designed for processing person related information collected from historical sources.
If you have an existing Kleio installation and want to share the files with git, you can do it by creating a new git repository in the directory containing the Kleio files.
Alternatively you can create a new repository with standard structure and copy your existing files to it (see this)
To share you repository with others you need to register them as collaborators in the repository. See this info.