I'm no expert on Safe but I believe this to be a namespace problem. I played with your code and produced:

use strict;

use Safe;

my $CODE = << 'END';

package A;

sub new {
  my($class) = @_;
  print "hi there";
  bless { }, $class;
}

package B; 

@ISA = qw(ROOT::A);

END

# If I uncomment this line, everything works.
# eval $CODE;

my $safe = Safe->new('ROOT');

$safe->reval($CODE);       
warn "code - $@" if $@;

ROOT::B->new();
warn "new - $@" if $@;
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Which prints the 'hi there' message. I don't think this is what you want, however. If you are wanting to load code and run it (from packages) then I would keep the package code in separate files and do the loading, run-time evaluation in the Safe compartment.

Now a disclaimer, this is how I do it but I don't know if there are any issues with it. I'd appreciate feedback :). If there is something wrong with this method then I've got some work to do on some of my projects :).

My way is slightly more complex cos I use a factory object to load the modules. Here is a stripped down version with that factory code removed.

use strict;
use warnings;
use Safe;

my $despatch = {};

my $code = sub
{
    my $module = "A";
    my $mainmodule = $module . ".pm";
    require $mainmodule; 
    import $mainmodule;    
    
    my $obj = $module->new();
    $despatch->{"A"} = $obj;
    
    $module = "B";
    
    $obj = $module->new();
    $despatch->{"$obj"} = $obj;
};
    
my $compartment = Safe->new('testing');
$compartment->reval(&{$code}());

$compartment->reval(
    $despatch->{'A'}->test()
);
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I put your module code in a file, called A.pm. I also added a method:

package A;

sub new {
  my($class) = @_;
  print "hi there\n";
  bless { }, $class;
}

sub test
{
    print "In test";
}

package B; 

@ISA = qw(A);
1;
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I know theres some useless variables (mainmodule etc) but they were all getting set via object methods and config file values so I left them in place.

All the best and I hope this helps.