public void run(){
     for(;;){
          if(isRunned){
               //continue to work
          }else{
             //a тут можете вызвать Thread.sleep  или wait();
          }
    }
}

t = new ThreadServer();

       buttonStart.addActionListener(new ActionListener(){

                @Override
                public void actionPerformed(ActionEvent e) {
                        t.start();
                }
            });

        buttonStop.addActionListener(new ActionListener(){

                @Override
                public void actionPerformed(ActionEvent e) {
                    t.suspendThread();
                }
            });

        resume.addActionListener(new ActionListener(){
                @Override
                public void actionPerformed(ActionEvent e) {
                    t.resumeThread();
                }
            });

    private class ThreadServer extends Thread{
        private boolean volatile isRunned;
        private Lock serverLock;
        private Condition readyoRunCondition = serverLock.newCondition();
        @Override
        public void run() {
       for(;;){
          if(isRunned){
               //continue to work new ChatServer();    
          }else{
            readyoRunCondition.await();
          }
    }

     public void suspendThread(){
           isRunned = false;
    }

public void resumeThread(){
      isRunned = false;
      readyoRunCondition.notifyAll();
}
    }