Within Teamwork Chat on your initial login as an external user you may find that you are unable to chat to other users and are seeing a blank chat window as below:
This is intended as a first time user. As an external company user you cannot write to anyone initially. It is only when a user in the owner company writes to you directly can you then only reply.
Once someone in the owner company adds you to a conversation or room, you can send messages in that conversation forever as long as you are not removed.
Note: As an external user, you cannot see other members of your own company in the people tab within the sidebar. Once someone in the owner company adds them to a conversation, they can then send messages in that conversation.
For more information see: Enabling and chatting to external company users