Irule or policy to URL rewrite

Can you give more details on url rewrite/translation. e.g. if incoming url is https://client.u.test.com/up/test1/test2, what should be the rewrite url?

There is still confusion around, how uri after /up should be translated. If you can provide more details on it then it would be clear. But I'm assuming those shouldn't be changed. Considering it won't change, you can use below iRule

when HTTP_REQUEST {
    set uri [string tolower [HTTP::uri]]
    switch -glob [string tolower [HTTP::host]] {
        "client.u.test.com" {
          if {$uri starts_with "/up" } {
		  HTTP::header replace "Host" "other.u.test.com"
		  pool Pool_other.u.test.com_1443
	      return
          }
	    }
       default {
	    return  
      }
    }
  }

If you need any other rewrite rule with uri after /up let me know and we can modify the iRule above

okay. You can use below

when HTTP_REQUEST {
    set uri [string tolower [HTTP::uri]]
    switch -glob [string tolower [HTTP::host]] {
        "client.u.test.com" {
          if {$uri starts_with "/up" } {
		  HTTP::header replace "Host" "other.u.test.com"
		  HTTP::uri /[join [lreplace [split [string trimleft [HTTP::uri] /] /] 0 0 "down"] /]
		  pool Pool_other.u.test.com_1443
	      return
           }
	  }
       default {
	    return  
      }
    }
  }

what error do you receive? Above iRule does the same where it will rewrite the HOST header and rewrite the url by replacing /up by /down and add all other uri after /down

Please enable logging in iRule to see what's happening?