Hi, In MHO, I would have suppose that you push, the data from $data variable into the variable $header_row instead the other way around, using unshift like you are doing. Something like so

...
 push @$header_row, @$data;
 print Dumper $header_row;
..
[download]

And of course, it gives you the same output like you had previously.
However, to have your desired out something like this works

use strict;
use warnings;
use Data::Dumper;

my $data = _test();

my $header_row;

push @$header_row, [ "City Name", "Last Name", "First Name", "Addrress
+", ],
  [ "", "", "", "", ];

my @values = qw(CITY LAST_NAME FIRST_NAME ADDRESS);

push @{$header_row} => [ map { @{$_}{@values} } map { @{$_} } @{$data}
+ ];

print Dumper $header_row;

sub _test {

    my @data = [
        {
            'CITY'       => 'San Frans',
            'LAST_NAME'  => 'Doe',
            'FIRST_NAME' => 'Jonh',
            'ADDRESS'    => '100 Main Street',
        },

    ];
    return \@data;
}
[download]

Output

$VAR1 = [
          [
            'City Name',
            'Last Name',
            'First Name',
            'Addrress'
          ],
          [
            '',
            '',
            '',
            ''
          ],
          [
            'San Frans',
            'Doe',
            'Jonh',
            '100 Main Street'
          ]
        ];
[download]

Since, you said you cannot change the subroutine _test()