You could construct an iterator.

use strict;
use warnings;

my @arr1 = qw{ tom harry diana nick sally henry };
my $iterator = do
   {
       my $idx = -1;
       my @actions = (
          sub { print qq{$_[ 0 ] plays\n} },
          sub { print qq{$_[ 0 ] eats\n} },
          sub { print qq{$_[ 0 ] sleeps\n} },
          );
       sub {
               $idx ++;
               $idx = 0 if $idx > $#actions;
               &{ $actions[ $idx ] };
           };
   };
$iterator->( $_ ) for @arr1;
[download]

The output

tom plays
harry eats
diana sleeps
nick plays
sally eats
henry sleeps
[download]

I hope this is of interest.

Update: Changed array @methods to @actions to avoid confusion since this is nothing to do with OO.