$_ = '<a href="foo">/path/sub/dir</a>';
$d = '/path';
$d = quotemeta $d;
print $1 if /"\s*>.*?$d(.*?)<\/A>/i;

# prints /sub/dir

# here it is with the regex expanded

$_ = '<a href="foo">/path/sub/dir</a>';
$d = '/path';
$d = quotemeta $d;
print $1 if m       # match regex
            /       # opening delim
            "       # literal "
            \s*     # plus 0 or more spaces
            >       # end of <a href tag
            .*?     # some leading stuff (minimum)
            $d      # our path
            (.*?)   # out subdirs captured into $1
            <\/A>   # the closing tag
            /ix;    # /i => case insensitive for </a> tag
                    # /x => allow comments