Try this

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1231884

use strict;
use warnings;
use Tk;
use Tk::NoteBook;
use Tk::Pane;

my (@packWidgetTopTitel) = qw/-side top -anchor w -pady 1m/;
my (@packWidgetTop) = qw/-side top -anchor w/;

my $CkAtSearchUserDatabase;
my $CkMergedWindow1;
my $CkMergedWindow2;
my $CkMergedWindow3;

my $mw = MainWindow->new();
my $book = $mw->NoteBook(-relief => 'flat')->pack(-side => 'top' , -ex
+pand => '1', -fill => "both", -ipadx => 6, -ipady => 6);  
  my $page1 = $book->add( "Sheet1", -label=>'left');
  my $page2 = $book->add( "Sheet2", -label=>'right');

  #left
  $page1->Label(-text => "OFF-LINE RESOURCES")->pack(@packWidgetTopTit
+el);
    $page1 -> Checkbutton(-text=>"My old data", -variable=>\$CkAtSearc
+hUserDatabase)->pack(@packWidgetTop);
  
  #right
  my $PaneT = $page2->Scrolled('Pane',
    -scrollbars => 'osoe',
    -sticky => 'nsew',
  )->pack(-anchor=> 'w', -fill => 'x');
    $PaneT->Label(-text=>"ON-LINE RESOURCES")->pack(@packWidgetTopTite
+l);
    $PaneT -> Checkbutton(-text=>"YXX", -variable=>\$CkMergedWindow1)-
+>pack(@packWidgetTop);  
    $PaneT -> Checkbutton(-text=>"XYX", -variable=>\$CkMergedWindow2)-
+>pack(@packWidgetTop);  
    $PaneT -> Checkbutton(-text=>"XXY", -variable=>\$CkMergedWindow3)-
+>pack(@packWidgetTop);  
MainLoop;
[download]

Here we are, tybalt89! I completely missed the -sticky option of the Pane! Thank you very much!