With the following minimal modifications to your code, it works.

I wouldn't advise using it as is particularly but if you can understand how the modifications make it work, you'll probably see a better way for doing this. (Hint: You won't need fork)

use strict;
use warnings;
use IO::Socket;
use threads;
use threads::shared;
use Thread::Queue;
use Tk;
$| = 1;


my $Q = new Thread::Queue; $Q->enqueue( 'Primer' );

my $server = IO::Socket::INET->new(
    LocalPort => 2345,
    Type      => SOCK_STREAM,
    Reuse     => 1,
    Listen    => 10
  )
  or die "Error: $@\n";

$SIG{CHLD} = sub { exit };
my $entry = "start...";
my $wsk   = \$entry;
my $main  = MainWindow->new( -title => 'Socket - listen', );
my $ent1  = $main->Label(
    -text => "I'm waitin on port 2345\n So, you tell me...",
)->pack();
my $ent2 = $main->Label(
    -text => $entry,
)->pack();
$main->repeat(
    100, sub{
        return unless $Q->pending;
        my $in = $Q->dequeue();
        $ent2->configure( -text => $in );
    }
);

my $child;
my $guzik1 = $main->Button(
    -text    => 'Exit',
    -command => sub { kill 9, $child; exit 0 },
)->pack( -side => 'bottom', );

$child = fork();
if ( $child == 0 ) {
    while ( my $client = $server->accept() ) {
        while ( defined( my $in = <$client> ) ) {
            #print $in;    #control
            $Q->enqueue( $in );
        }
    }
}

MainLoop()
[download]