How can an atheist rest in peace?

The position of an atheist is a rejection of all god claims. As such, (I will assume you mean the Christian belief of an afterlife for this question) an Atheist does not believe in afterlife or heaven and hell claims. It is unknown what happens after you die. One might just simply cease to exsist. This may seem uncomfortable, but that doesn't mean, for an Atheist, they're willing to act on unsubstantiated "faith" claims.