How do I draw on a JPanel from multiple outside classes?

I am currently making a game with a main menu and a world where you actually play.

I have a class called Game, which inherits from JPanel and implements the Runnable, MouseListener, KeyListener and ActionListener interfaces (only important parts included)

I also have two classes InWorldHandler and OutWorldHandler for handling the mechanics in the world and outside of it respectively.

The Game class:

public class Game extends JPanel implements Runnable, KeyListener, MouseListener, ActionListener
{
    protected JFrame frame;
    private Timer timer = new Timer(25, this);

    private World world;
    private Player player = new Player();

    private boolean draw;

    Game(World world)
    {
        frame = new JFrame("Minecraft 2D");
        this.world = world;
        player.enterWorld(world, this);
    }

    @Override
    protected void paintComponent(Graphics g)
    {
        Graphics2D g2d = (Graphics2D)g;

        if(draw)
        {
            g2d.setColor(new Color(255, 255, 255));
            g2d.fillRect(0, 0, frame.getWidth(), frame.getHeight());

            draw = false;
            //Here, the in-game mechanics should be handled
            if(player.inWorld())
            {
                Chunk chunk = player.getLoadedChunk();
                for(int x = 0; x < 16; x++)
                {
                    for(int y = 0; y < 16; y++)
                    {
                        Block block = chunk.getBlockAt(x, y);
                        BufferedImage texture = block.getTexture();

                        g2d.drawImage(block.getTexture(), x*32, y*32, texture.getWidth()*2, texture.getHeight()*2, null);
                    }
                }
            }
            //Here, the out-game mechanics should be handled
            else
            {

            }
        }
    }

    @Override
    public void actionPerformed(ActionEvent e)
    {
        this.repaint();
        draw = true;
    }

    @Override
    public void run()
    {
        draw = true;

        frame.setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);
        frame.add(this);
        frame.setMinimumSize(new Dimension(518, 540));
        frame.setResizable(false);
        frame.setLocationRelativeTo(null);
        frame.addKeyListener(this);
        frame.addMouseListener(this);
        frame.setFocusable(true);
        frame.setVisible(true);
        frame.pack();
        timer.start();
    }
}

Both the other classes have empty bodies currently. I just have no idea how to do that.

I want the InWorldHandler class to draw on the panel when the player is in game, and the OutWorldHandler class when the player is in the main menu, both called in the Game class. How do I do that?

Instead of having a single JPanel, why don't you try with a CardLayout and switch whether to show the InnerWorld or the OuterWorld according to a flag that determines where in the program you're at.

As you're implementing KeyListener, I think that's for you to be able to move your character, please take a look at the accepted answer on this question: Keylistener not working for JPanel and use KeyBindings instead.

Also avoid the use of setMimimum/Maximum/PreferredSize() and override those methods instead: Should I avoid the use of set(Preferred|Maximum|Minimum)Size methods in Java Swing?

Take this code as an example:

import java.awt.BorderLayout;
import java.awt.CardLayout;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Graphics2D;

import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.SwingUtilities;

public class Game {
    private JFrame frame;
    private JButton button;
    private boolean status;
    private JPanel[] cards;
    private CardLayout cl;
    private JPanel gamePane;

    public static void main(String[] args) {
        SwingUtilities.invokeLater(() -> new Game().createAndShowGUI());
    }

    private void createAndShowGUI() {
        frame = new JFrame(getClass().getSimpleName());
        button = new JButton("Switch Worlds");
        status = true; //True = Inner / False = Outer

        cl = new CardLayout();

        gamePane = new JPanel(cl);
        cards = new JPanel[2];

        cards[0] = new InnerWorld();
        cards[1] = new OuterWorld();

        gamePane.add(cards[0], "innerWorld");
        gamePane.add(cards[1], "outerWorld");

        button.addActionListener(e -> {
            status = !status;
            if (status) {
                cl.show(gamePane, "innerWorld");
            } else {
                cl.show(gamePane, "outerWorld");
            }
        });

        frame.add(gamePane);
        frame.add(button, BorderLayout.SOUTH);

        frame.pack();
        frame.setVisible(true);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    }
}

@SuppressWarnings("serial")
class InnerWorld extends JPanel {
    @Override
    protected void paintComponent(Graphics g) {
        super.paintComponent(g);

        Graphics2D g2d = (Graphics2D) g;

        g2d.drawString("Inner World", 50, 50);
    }

    @Override
    public Dimension getPreferredSize() {
        return new Dimension(200, 200);
    }
}

@SuppressWarnings("serial")
class OuterWorld extends JPanel {
    @Override
    protected void paintComponent(Graphics g) {
        super.paintComponent(g);

        Graphics2D g2d = (Graphics2D) g;

        g2d.drawString("Outer World", 50, 50);
    }

    @Override
    public Dimension getPreferredSize() {
        return new Dimension(200, 200);
    }
}