Your current code does not make thread except application's main
thread.

Java GUI runs as a single thread. If you do a long and time consuming
task, such as your for(;;) loop, your single app thread is fully
occupied by the task and GUI can't have its turn to run.

Long and time consuming task should be run as a new separate thread.
Try this code:
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/*
<applet code="Sagar" width="200" height="50"></applet>
*/
import java.applet.*;
import java.util.*;
import java.awt.*;

public class Sagar extends Applet{
 String ds;

 public void start(){
   new Thread(){
     public void run(){
       while (true){
         ds = (new Date()).toString();
         repaint();
         try{
           Thread.sleep(1000);
         }
         catch (InterruptedException e){
           e.printStackTrace();
         }
       }
     }
   }.start();
 }

 public void paint(Graphics g){
   g.drawString(ds, 10, 10);
 }
}
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