How to solve such a problem with proxying?

Question

ubuntu

There is a server, let's say SERVER1. It runs a service. Receives requests and responds. There was a need to transfer the service to another server [SERVER2] WITHOUT interruption in work until the DNS is updated.
There is such an idea. Raise a proxy on SERVER1, which would transfer all requests to SERVER2 and return responses to the user. When DNS is updated - SERVER1 can be bang.
The question is: how to do it? What proxy software to use. Preferably as easy as possible.
Thank you.

Answer 1

Understood. Thanks for the tip. For those who may need this, here is the solution: nginx.conf

worker_processes  1;

events {
    worker_connections  1024;
}

stream  {
    server {
        listen 127.0.0.1:PORT;
        proxy_pass SERVER2:PORT;
    }
}

Answer 2

nginx config - 

        location / {
            proxy_pass http://SERVER2;
        }