You could use ansible to deploy and run chef-client.
$ ansible -i hosts all -a 'chef-client'
ansible is easily installed with pip:
pip install ansible
Your inventory file (in the example, named "hosts") might look like this:
[all]
host1.example.com ansible_user=root
host2.example.com ansible_user=root
host3.example.com ansibel_user=root
(notice "all" is the name of the grouping in the configuration file for our example - this is arbitrary and can be anything. Your inventory file can also include other groupings as well, eg [web_wervers], [database_servers], [chef_servers], etc.)
So,again, putting it all together:
> ansible -i hosts all -a 'chef-client'
or maybe:
> ansible -i hosts all -a 'systemctl status'