To get some code called whenever Entry1 changes, you can set up a validation callback.

my $entry1 = $parent->Entry(
    -validate => 'all',
    -validatecommand => sub {
        my $newvalue = shift;
        $entry2_value = length $newvalue; # set value of Entry2
        return 1; # return true to allow the entry value to change
    },
    # other args...
);
[download]

Make sure your callback code returns true, to say that the new value is valid and allow it to change.

Also, the other part to mention is that  $entry2_value could be the  -textvariable (see Tk::options) of the Entry2 widget, thus automatically updating the entry.