Is this what you want?

use strict;
package A;

sub new {
    my $class = shift;
    bless {}, $class;
}

sub test {
    "original test"
}
sub do_alias {
    my $self = shift;
    *test_alias = \&test;
}
sub redefine_alias {
    my $self = shift;
    *test_alias = sub {"new test"};
}

package main;

sub say { print @_,"\n" }

my $a = new A;
say $a->test();        # test
$a->do_alias(); 
say $a->test_alias();  # test
$a->redefine_alias();
say $a->test_alias();  # new_test
say $a->test();        # test
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Best regards