document.querySelector(".clickedelement").addEventListener("click", function (e) {
  setTimeout(function(){
  if(document.querySelector(".my-div-class").style.border !== "none"){
      document.querySelector(".my-div-class").style.border = "none";
  }else{
    document.querySelector(".my-div-class").style.border = "1px solid black";
  }
  },1000);
});

div {
  width: 100px;
  height: 100px;
  background-color: yellow;
  border-radius: 50%;
}

<p class="clickedelement">when this is <b>clicked</b> i want border added and removed (after 1s) on div below</p>
<div class="my-div-class"></div>