VIP redirect to another VIP

Certainly. There are at least two ways:

1. Explicit HTTP redirect - this is where you issue an explicit 302 redirect to send the client browser somewhere else. It can be done with an iRule, an HTTP class (11.3 and below), or a policy (11.4 and above). It's actually a pretty common use case to redirect from an HTTP VIP to an HTTPS VIP. So common in fact that there's a built-in iRule for it. It might look something like this:

   when HTTP_REQUEST {
       if { ...some condition... } {
           HTTP::redirect "https://somewhere.else.com"
       }
   }
   

   You can also use the HTTP::respond command for a bit more flexibility.

   when HTTP_REQUEST {
       if { ...some condition... } {
           HTTP::respond 301 Location "https://somewhere.else.com"
       }
   }
   

2. VIP targeting - this is where you basically put one VIP in front of another one. The external VIP would have your publicly-accessible destination IP and port, and would forward the traffic to the internal, potentially non-routable VIP via an iRule and the virtual command. Here's an example:

   when HTTP_REQUEST {
       if { ...some condition... } {
           virtual internal-vs
       }
   }
   

   where "internal-vs" is the name of the internal VIP.