iRule to block anything containing /user thats not coming for internal network

I assume you still want to match the Host header and you want to match anything starting with "/user":

when HTTP_REQUEST { 
    if { [string tolower [HTTP::host]] eq "domain.name.com" and not ([class match [IP::client_addr] equals sntru_net]) } {
        switch -glob [HTTP::path] {
            "/user" -
            "/user/*" {
                discard
            }
        }
    }
}

You don't need the

default

branch because selection of the assigned pool is what will happen by default already.

I assume you still want to match the Host header and you want to match anything starting with "/user":

when HTTP_REQUEST { 
    if { [string tolower [HTTP::host]] eq "domain.name.com" and not ([class match [IP::client_addr] equals sntru_net]) } {
        switch -glob [HTTP::path] {
            "/user" -
            "/user/*" {
                discard
            }
        }
    }
}

You don't need the

default

branch because selection of the assigned pool is what will happen by default already.