In this example the Foo class is part of the library

Foo.java

1. import processing.core.*;
2. 
   
3. PApplet app; // always useful to have a reference to the applet
4. PGraphics pg;
5. 
   
6. public class Foo {
7.       
8.       public Foo(PApplet papplet){
9.             app = papplet;
10.       }
11. 
    
12.       public void createGraphicContext(int w, int h, String mode){
13.             pg = app.createGraphics(w, h, mode);
14.             pg.beginDraw9);
15.             pg.background(255); // clear to white
    
16.             pg.endDraw();
17.       }
18. }

Then in  the sketch

1. Foo foo;
2. void setup(){
3.       size(800, 600, OPENGL);
4.       foo = new Foo(this);
5.       foo.createGraphicContext(this, width, height, OPENGL);
6. }

Mode can be JAVA2D, P2D, P3D or OPENG

AFAIK the last three are all based on OPENGL which means if you want pg to be one of these then the sketch must also use an OpenGL based renderer.