First of all, both the old key and the new key should refer to a reference. If $clients{$old_key} is a reference, there's no need to take the address in the assignment to $new_client_hash{$old_key}. On the other hand, if $clients{$old_key} is a value, both assignments to $new_client_hash should be of the address.

I'd do something like

  my $value = $clients{$old_key};
  $new_client_hash{$new_key} = \$value;
  $new_client_hash{$old_key} = \$value;
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to avoid confusion if $clients{$old_key} holds the value,

  $new_client_hash{$new_key} = $clients{$old_key};
  $new_client_hash{$old_key} = $clients{$old_key};
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if it's a reference.

Just my 2 cents, -gjb-