The following does what you want, although I don't think it's particularly pretty. I think that XML::Twig (as recommended by Cristoforo), or at least XML::LibXML would be much better. Note that both XML::XPath and XML::Twig use the same underlying parser, XML::Parser, which in turn uses Expat.

use warnings;
use strict;
use XML::XPath;

my $xml = <<'ENDXML';
<includes>
    <include>
        <priority>9990</priority>
        <required>true</required>
        <location>/efs/dist/tpcommon/itrstemplates/latest/common/templ
+ates/equities.xml</location>
    </include>
    <include disabled="true">
        <priority>10001</priority>
        <required>true</required>
        <location>/efs/dist/itrs/tools/latest/common/templates/global_
+authentication.xml</location>
    </include>
</includes>
ENDXML

my $xp = XML::XPath->new(xml => $xml);
my $nodes = $xp->find('//includes/include');
for my $include ($nodes->get_nodelist) {
    for my $p ($xp->findnodes('./priority', $include)) {
        my $priority = $p->string_value;
        $p->removeChild($_) for $p->getChildNodes;
        $p->appendChild( XML::XPath::Node::Text->new($priority+1) );
    }
}
my ($root) = $xp->findnodes('/');
print $root->toString, "\n";
[download]

In regards to the last two lines above, I haven't yet found an easy way to print back out the XML document, maybe I'm missing something obvious. Anyway, for comparison, here's an XML::Twig solution:

use XML::Twig;
open my $ofh, '>', \my $outxml or die $!;
my $twig = XML::Twig->new(
    twig_print_outside_roots => $ofh,
    twig_roots => {
        '/includes/include/priority' => sub {
            my ($twig, $elt) = @_;
            $elt->set_text( $elt->text+1 );
            $elt->flush($ofh);
        },
    } );
$twig->parse($xml);
close $ofh;
print $outxml;
[download]

I've written some things a little longer than they need to be in this code for clarity, the code could be shortened quite a bit, and also the output doesn't need to go to a string, it could be sent to a file directly.