F5 Redirect HTTP traffic to different ports based on context root

This can be achieve via iRule or F5 Policy.

Create the Pool based on the port wise and route the traffic on URI pattern. .

Example: Pool_8081 [ Member : 21.12.3.8:8081],

Pool_8082[ Member : 21.12.3.8:8082]

And route the traffic based on pattern. This is an example you can modify based on requirements

when HTTP_REQUEST {
set uri [string tolower [HTTP::uri]]
switch -glob $uri {
      "/example1/*" {
       pool Pool_8081
      "/example2/*" {
       pool Pool_8082
      }
   }
}

Cheers..