Clayton itself has no beach in which to surf. But, like almost anywhere in Panama, you can drive from Clayton to the beach to surf.
The best surf in Panama is in Venao. That is where people go to surf. Venao is a long way from Clayton. It is just south of Pedasi and I think it takes about 5 to 6 hours to get there from Clayton by car.
If you want to go surfing at a beach that is closer to Clayton, I think you could go to Playa Teta, which is about 2 hours away from Clayton but Venao is the best. People who really love surfing go to Venao.