Many atheists don’t, but it is not a requirement of atheism. The only thing that determines whether or not you are an atheist is whether or not you believe in the existence of a god.
Most atheists take the same position with regards to an afterlife as they do with regards to a god: there is no proof that an afterlife does exist, but there is no proof that an afterlife doesn’t exist either – so they neither believe that it does nor believe that it doesn’t exist. They maintain a position of scepticism.