From the docs,

$text: The remaining (unparsed) text. Changes to $text do not propagate out of unsuccessful productions, but do survive successful productions.

So we need to remove from $text what the query parser matches. Also from the docs,

If, however, the text to be matched is passed by reference [...] then any text which was consumed during the match will be removed from the start of [the referenced string].

So it's quite simple:

$TemplateParser = Parse::RecDescent->new(<<'__GRAMMAR__');

   template:  identifier 'TEMPLATE' '{' statement(s) '}'

   statement: expression
            | conditional
            | loopcontrol
            | { $QueryParser->query(\$text) }

__GRAMMAR__
[download]

Tested.