package Foo;

use base qw(CGI::Application);
use Bar;

sub new {
     my $class = shift;
     # SUPER refers to CGI::App because of 'use base'
     my $self = $class->SUPER::new(); 
     $self->{ stuff } = 'whatever';
     $self->{ bar } = Bar->new(); # I wouldn't use 'super' as a key here
     return $self;
}

# etc ...

##</code><code>##

use Foo;

my $app = Foo->new();