Well if you can change the 'my' to 'our' in p1 then this works

Package 1

package p1;

our $var1 = 'var1-p1';#Note the change my->our

sub new {
    my $class = ref $_[0] ? ref shift : shift;
    my $self = {};
    bless $self, $class;
    return $self;
}

sub get_var1 {
    return $var1;
}

1;
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Package 2

package p2;

use p1;

our @ISA=qw(p1);

sub set_var1 {
    my $self = shift;
    my $new_var1 = shift;
    $p1::var1 = $new_var1;
    return $p1::var1;
}

1;
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You get a global variable that you may not want

You only need to change my $var1 ... to our $var1 ... and adapt p2, but maybe your real p1-module is much more complicated?

The patch of p2.pm below seems to work without changing p1.pm on disk, but I wouldn't recommend it for production.

Rather try to fix the root problem, e.g. ask the module author or use a private modified copy of the module and use use lib or $PERL5LIB so the patched version is found first.

#-- p1 not changed on disk ;-)
use File::Slurp;
my $text = read_file( 'p1.pm' ) ;
$text =~ s/^\s*my(\s+\$var1)/our$1/ms;
eval $text;
#-- above not recommended!

package p2;

#  use p1;

our @ISA=qw(p1);

sub set_var1 {
    my $self = shift;
    my $new_var1 = shift;
#   $var1 = $new_var1;
#   return $var1;
    $p1::var1 = $new_var1;
    return $p1::var1;
}

1;
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