Redirect HTTP along with header

You can try below

when HTTP_REQUEST {
    switch -glob [string tolower [HTTP::host]] {
	  "service-api.xx.com"
	   {
	    if { [HTTP::header exists "Auth_header"] } {
        set token [HTTP::header value Auth_header]
		HTTP::respond 301 Location https://newservice.api.xx.com/test-cg[HTTP::uri]" "Auth_header" "$token"
		return
           }
           } default {
          return
      }
    }
 }