There is no need to add a dragstart handler on an element that contains text.
Any selected text is automatically added to the clipboard with a name/key equal to "text/plain". Just add a drop event handler on the drop zone and fetch the data from the clipboard using "text/plain" as the access key:
function drop(target, event) {
event.preventDefault();
target.innerHTML = event.dataTransfer.getData('text/plain');
};
Try it in your browser below (select text, then drag and drop it into the drop zone) or play with it at CodePen: