The main problem is that you aren't using a variable for -textvariable for the label. The code below fixes that and also passes a reference to the variable through to the sub that updates its contents:

#!/usr/bin/perl 
use warnings;
use strict;

use Tk;


my $mw = new MainWindow;
my $time;
my $label = $mw->Label(-textvariable => \$time);
$label->grid(-row => 1, -column => 1);

$mw->repeat(1000, sub {timer (\$time)});

MainLoop;


sub timer {
    my ($varRef) = @_;
    
    $$varRef = time();
}
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