Well, the regex and split will certainly work. I'd like to provide two more options for you.

The first uses index and substr. This has the advantage of being very fast (often faster than regex -- regexes can do more, though). I don't know if it's faster than split (probably not), but there may be reasons for you to use it.

my $string = '(<some word> | No Qualifier | <some word> | <some word>'
+;
my $start = index( $string, '|' );          # find first pipe position
my $end = index( $string, '|', $start+1 );  # find next pipe position

my $qualifier = substr( $string, $start, $end-$start+1 ); # extract
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The second suggestion I have is a bit more robust, and leverages the module Text::CSV_XS. You'd use this approach if you have, e.g. a file of lines that look like your example -- and especially if you're interested in more than one field in that line, and/or if your data might have escaped pipes in it.

use IO::File;
use Text::CSV_XS;

my $csv = Text::CSV_XS->new({ sep_char=>'|' });
my $io  = IO::File->new('myfile.piped.txt', '<') or die "Can't read fi
+le: $!\n";

until ($io->eof) {
    my $row = $csv->getline($io);  # read and parse line into an ARRAY
+ref
    print "Second field says: ", $row->[1], "\n";
}
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Even if your data isn't in a file, Text::CSV_XS can parse it for you; it's worth looking into.