removing part of uri in redirect

Is "/application" a literal and consistent URI value, or just a representation of multiple possible values? If the former, then a simple string map should suffice:

when HTTP_REQUEST {
     if { [HTTP::uri] starts_with "/application" } {
          HTTP::uri [string map {"/application/" "/"} [HTTP::uri]]
     }
}

This will transparently change all incoming requests. If you need something more robust, perhaps changing outgoing URIs and links, then I'd suggest either looking at the ProxyPass iRule or the 11.4's new rewrite profile.