I see that no one responded to your question so I'll take a shot to bump it back up to the first page.
It sounds like sensory-seeking behavior. Can you find a replacement, for example patting a pillow? Can you use the clapping to teach clapping games and work on interaction?
My youngest son goes through phases of hand clapping. I'm honestly not certain if it's a visual thing, an auditory thing, a tactile thing, or a combination of all. When my son does it, he claps really fast and watches his hands move. Telling him "quiet hands" helps a bit, but most of the time he just can't help himself.
We used to do brushing with both boys. I dug out one of the brushes and started brushing his hands when he felt the need to clap. I tell him we're going to "wake up" his hands. It actually helped quite a bit. I think he probably claps primarlily for the sensory input to his hands. There is a visual component, but I think it's a secondary thing for him.
Good Luck!Brushing helped here as well with the clapping. Another thing is my son loves gloves so we bought several different kinds with different textures and we let him wear them. It dampens the clapping sound and it also gives him sensory input because of the different textures on the gloves that he gets while clapping. Another option is pillow or stuffed animal clapping where he holds the pillow or stuffed animal and claps.
Have you tried one of those little hackey sack balls...about two inches across? The party stores carry them as party favors, usually six to a pack, and they come in soccer, baseball, etc patterns. They make clapping lots quieter!
Cole likes to pat small, pliable objects between his hands, up at chin level, but sometimes it IS clapping and saying EEEEEEEEEEE EEEEEEEEEEEE EEEEEEEEEEEE. The noise of the stimming drives me bats, so I try to get him to say A E I O U, A E I O U, in this little melody I made up.
Let me know if you find the holy grail on this one! I need it too!