Can an application initiate behind an F5? If so, what is that called and how does it work? Is a special irule needed?

My application team wants to know if an application can initiate transfer behind an F5. Currently our server points to a VIP at the client side, I guess our server "fills up" and we have to stand up a new server, and it takes a week or more for the client change process to allow our new server ip into their network (firewall changes most likely). We'd like to avoid that by being able to add / change pool members behind a VIP. Is a special Irule needed for this? Is there a certain type of style / name for this type of application?

Again - we initiate the app by transferring data, and the client has VIP listening for us to connect.

Thanks, Ken N.