He is wearing a banyan and banyan cap, 18th century mens sleepwear. A banyan is a loose robe of simple design, like a bathrobe made of very expensive material. Perhaps more like a smoking jacket, if you've seen those. The design of the cap is based on Persian clothing, you can tell by the tassels.
Now, men wouldn't wear these to bed, but something comfortable to lounge around the house in. Gentry took their sweet time getting dressed in the morning and might recieve callers in their banyan if they were feeling casual.
Wikipedia has more to say about them
Can you tell what that is on the far right? I will be very surprised if you guess.