It takes two to tango, and I find the clients who like to stay on for a chat are under the impression that I want a chat too. That usually means I am responding to something provocative that they are saying, and in turn I must be feeding them conversation they latch onto.
This takes personal discipline - however engaging the conversation, I have to take my own attention out of it, and if the client continues, then I just look at my watch and say 'Sadly I have to leave it there'.
Occasionally, if that isn't enough, I have caught myself saying 'I'm afraid I'm going to have to boot you out now, very nice to see you again'. They don't get offered tea -there is a cafe nearby. They get offered water.
For early arrivals, I make it quite clear 'I'm not quite ready for you, make yourself comfortable and I'll be with you shortly'. I then leave them alone and get on with something else, if that is what I need to do, eg preparing the room.
Obviously, if I am happy to see them early, I will always ask them first - some people have ten minutes texting or reading to catch up on while waiting. Their earliness does not mean they are ready either.
In the case of your specific client, you may have to play tonight by ear, but for future bookings, make it clear they are being 'fitted in to a slot' from the start, tell them when it starts and when it finishes, and act like you mean it.
These disciplines help our client as well as us - many have problems that mean they expect others to orbit around their own scattiness. Not healthy to get sucked into their problems, be the solid base they need, not the shifting sands they expect.