You are chomping the line, even though you never look at anything other than the first record on the line if its not valid, then catenate a newline back to the end of it on saving it. You repeatedly open/close files for single records. Your regex has a quantifier of {9} although you already made sure only to look at the first nine characters - a double negative is more economic in that case (test for the absence of non-digit characters).

Also, you can reduce quite a lot of duplication.

my (%handle, $fh, $count);
$handle{02} = \*OUTPUT;

while(my $line = <INPUT>) {
    if(substr($_, 0, 9) !~ /\D/) {
        chomp $line;

        my $year;
        ($line, $year) = validLine($_);
        $line .= "\n";

        $count = $year ne "02" ? \$y_count : \$o_count;
        $fh = $handle{$year} || do {
            open my($newfh), ">>", $path."year$year.txt"
                or die "Cannot open file: $!\n";
            $newfh;
        };
    }
    else {
        $fh = \*DISCARD;
        $count = \$d_count;
    }
      
    ++$$count;
    print $fh $line;
}
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If you post your validLine, chances are improvements to it can also be suggested.

Makeshifts last the longest.