It’s not possible to bill a contact in Karbon that’s setup as a Client Group, but if you setup the entity as a normal contact (Organisation) in Karbon, you can bill it. Is the entity a real entity? 

For example:

Client Group: ABC Pty Ltd Group (group members are ABC Pty Ltd and Alan B. Collins)

Organisation: ABC Pty Ltd

Person: Alan B. Collins

Bill everything to ABC Pty Ltd (you can choose ABC Pty Ltd as the Bill To entity for ABC Pty Ltd Group and Alan B. Collins)

We made the mistake of making actual entities represented as client groups in our early days and quickly learned that client groups are for a specific purpose (they represent non-real collections of real entities), and you can bill time to them, but you must set the bill-to to one of the actual entities, like @SamG explained above.