Thank you for your patience. I have checked it with our Product team and found out that the GroupDocs.Signature for Cloud doesn't has such feature currently but we can add it as a new feature if you will provide more info about what you need and how it should work. For example should it be some sort of an input field (placeholder) where the user data will be entered after signing or this info should be added to the signature.
Please provide detailed description for this feature and I will discuss it with Product team.
Also will be very useful if you will provide an example of the word template with the "CLIENT SIGNATURE:" short code that you use.