You can use a method:

package Foo;
my %Required;
BEGIN {
    @Required{qw(This That TheOther)}= (1)x3;
}
sub _GetRequired {
    return \%Required;
}
# ...
package Base;
sub _GetRequired {
    return {};
}
sub isRequired {
    my $self = shift;
    my $attr = shift;
    return $self->_GetRequired()->{$attr};
}
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(Updated.)

        - tye (but my friends call me "Tye")