How do I perform a JAVA callback between classes? [duplicate]

Define an interface, and implement it in the class that will receive the callback.

Have attention to the multi-threading in your case.

Code example from http://cleancodedevelopment-qualityseal.blogspot.com.br/2012/10/understanding-callbacks-with-java.html

interface CallBack {                   

//declare an interface with the callback methods, 
//so you can use on more than one class and just 
//refer to the interface

    void methodToCallBack();
}

class CallBackImpl implements CallBack {          

//class that implements the method to callback defined 
//in the interface

    public void methodToCallBack() {
        System.out.println("I've been called back");
    }
}

class Caller {

    public void register(CallBack callback) {
        callback.methodToCallBack();
    }

    public static void main(String[] args) {
        Caller caller = new Caller();
        CallBack callBack = new CallBackImpl();       

//because of the interface, the type is Callback even 
//thought the new instance is the CallBackImpl class. 
//This alows to pass different types of classes that have 
//the implementation of CallBack interface

        caller.register(callBack);
    }
} 

In your case, apart from multi-threading you could do like this:

interface ServerInterface {
    void newSeverConnection(Socket socket);
}

public class Server implements ServerInterface {

    public Server(int _address) {
        System.out.println("Starting Server...");
        serverConnectionHandler = new ServerConnections(_address, this);
        workers.execute(serverConnectionHandler);
        System.out.println("Do something else...");
    }

    void newServerConnection(Socket socket) {
        System.out.println("A function of my child class was called.");
    }

}

public class ServerConnections implements Runnable {

    private ServerInterface serverInterface;
    
    public ServerConnections(int _serverPort, ServerInterface _serverInterface) {
      serverPort = _serverPort;
      serverInterface = _serverInterface;
    }

    @Override
    public void run() {
        System.out.println("Starting Server Thread...");

        if (serverInterface == null) {
            System.out.println("Server Thread error: callback null");
        }

        try {
            mainSocket = new ServerSocket(serverPort);

            while (true) {
                serverInterface.newServerConnection(mainSocket.accept());
            }
        } catch (IOException ex) {
            Logger.getLogger(Server.class.getName()).log(Level.SEVERE, null, ex);
        }
    }
}

Multi-threading

Remember this does not handle multi-threading, this is another topic and can have various solutions depending on the project.

The observer-pattern

The observer-pattern does nearly this, the major difference is the use of an ArrayList for adding more than one listener. Where this is not needed, you get better performance with one reference.