The thingies one creates with use constant are subs, so you could just inherit them like any other method:

use strict;
use warnings;

package Foo::Constants;
use constant PI => 3.1415826;

package main;

@Foo::Base::ISA = qw( Foo::Constants );
@Foo::Sub::ISA  = qw( Foo::Base );

@Bar::Sub::ISA  = qw( Foo::Sub );
sub Bar::Sub::new {
  my $class = shift;
  print $class->PI, $/;
}

Bar::Sub->new();
__END__
3.1415926
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